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Journal articles on the topic 'Markov Transition Matrix'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Strzempko, Jessica, and Robert Gilmore Pontius. "The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix." Land 12, no. 7 (2023): 1471. http://dx.doi.org/10.3390/land12071471.

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The Flow matrix is a novel method to describe and extrapolate transitions among categories. The Flow matrix extrapolates a constant transition size per unit of time on a time continuum with a maximum of one incident per observation during the extrapolation. The Flow matrix extrapolates linearly until the persistence of a category shrinks to zero. The Flow matrix has concepts and mathematics that are more straightforward than the Markov matrix. However, many scientists apply the Markov matrix by default because popular software packages offer no alternative to the Markov matrix, despite the con

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2

Dukhovny, Alexander M. "Markov chains with quasitoeplitz transition matrix." Journal of Applied Mathematics and Simulation 2, no. 1 (1989): 71–82. http://dx.doi.org/10.1155/s1048953389000055.

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This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories) with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.

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3

Solan, Eilon, and Nicolas Vieille. "Perturbed Markov chains." Journal of Applied Probability 40, no. 1 (2003): 107–22. http://dx.doi.org/10.1239/jap/1044476830.

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We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

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4

Solan, Eilon, and Nicolas Vieille. "Perturbed Markov chains." Journal of Applied Probability 40, no. 01 (2003): 107–22. http://dx.doi.org/10.1017/s0021900200022294.

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We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

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5

F. Ahmed, Alaa. "A Proposed Bayesian Estimation of Transitional Probability for a Markov Chain with Random Times via Swarm Algorithm." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ) 56, no. 1 (2025): 411–20. https://doi.org/10.55562/jrucs.v56i1.37.

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The transition matrix estimators of the Markov chain are not accurate and the transition matrix is considered given. There are many methods that are used to estimate the transition probabilities matrix for different cases, the most famous of which is the Maximum Likelihood Method, in order to find a good and new estimator for the transition probabilities matrix of the Markov chain, a method was proposed, which is a modification of the Bayes method, to reach the transition probabilities with the least variance. This method assumes that the values of in the initial probability are estimated by t

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Eastman, J. Ronald, and Jiena He. "A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling." Land 9, no. 11 (2020): 407. http://dx.doi.org/10.3390/land9110407.

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Land change models commonly model the expected quantity of change as a Markov chain. Markov transition probabilities can be estimated by tabulating the relative frequency of change for all transitions between two dates. To estimate the appropriate transition probability matrix for any future date requires the determination of an annualized matrix through eigendecomposition followed by matrix powering. However, the technique yields multiple solutions, commonly with imaginary parts and negative transitions, and possibly with no non-negative real stochastic matrix solution. In addition, the compu

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7

Rothe, Frederic, and Martin Lames. "Markov-chain Modelling and Simulative Assessment of the Impact of Selected Tactical Behaviours in Modern Tennis." International Journal of Racket Sports Science 5, no. 1 (2023): 1–13. https://doi.org/10.30827/ijrss.33243.

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Game behaviour in net games or other sports is often captured in the form of discrete performance indicators which represent frequencies or relative frequencies of key behavioural variables. In this regard however, discrete performance indicators are often of low practical relevance as they lack information on the sequence of actions and the underlying interaction of players in a match. Thereby, establishing a connection between performance indicators and sport success also remains an open challenge. In tennis, finite Markov chain modelling based on a transition matrix has shown promise in cir

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8

Ghaffari Rad, Afsaneh, Sajjad Negahban, Behzad Tokhmechi, and Hossein Mostafavi. "DRILL BIT SELECTION IN A FORMATION WITH DIFFERENT SEDIMENTARY FACIES USING THE MARKOV CHAIN: A CASE STUDY AT ONE OF THE OIL FIELDS IN THE SOUTH OF IRAN." Rudarsko-geološko-naftni zbornik 36, no. 2 (2021): 83–92. http://dx.doi.org/10.17794/rgn.2021.2.8.

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The selection of a drill bit is an essential issue in well planning. Furthermore, identification and evaluation of sedimentary rocks before well drilling plays a crucial role in choosing the drill bit. Moreover, the Markov chain as a stochastic model is one of the powerful methods for identifying lithological units, which is based on the calculation of the transition probability matrix or transition matrix. The Markov chain experiences transitions from one state (a situation or set of values) to another according to specified probabilistic rules. In this paper, the Markov chain was implemented

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9

Hartfiel, D. J. "Homogeneous Markov chains by bounded transition matrix." Journal of Applied Probability 31, no. 2 (1994): 362–72. http://dx.doi.org/10.2307/3215029.

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Let A be a stochastic matrix and ε a positive number. We consider all stochastic matrices within ε of A and their corresponding stochastic eigenvectors. A convex polytope containing these vectors is described. An efficient algorithm for computing bounds on the components of these vectors is also given. The work is compared to previous such work done by the author and by Courtois and Semai.

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10

Hartfiel, D. J. "Homogeneous Markov chains by bounded transition matrix." Journal of Applied Probability 31, no. 02 (1994): 362–72. http://dx.doi.org/10.1017/s0021900200044880.

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Let A be a stochastic matrix and ε a positive number. We consider all stochastic matrices within ε of A and their corresponding stochastic eigenvectors. A convex polytope containing these vectors is described. An efficient algorithm for computing bounds on the components of these vectors is also given. The work is compared to previous such work done by the author and by Courtois and Semai.

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11

Dukhovny, A. M. "Markov chains with quasitoeplitz transition matrix: applications." Journal of Applied Mathematics and Stochastic Analysis 3, no. 2 (1990): 141–52. http://dx.doi.org/10.1155/s1048953390000120.

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Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ( warm-up, switch at threshold etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and MI/G/1 types with arbitrary random sizes of arriving and departing groups are studied.

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12

Mohamed, Mohamed, Mohamed Bisher Zeina, and Yasin Karmouta. "Classification of States for Literal Neutrosophic and Plithogenic Markov Chains." Journal of Neutrosophic and Fuzzy Systems 08, no. 2 (2024): 49–61. http://dx.doi.org/10.54216/jnfs.080206.

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In this paper we represent many classifications of neutrosophic and plithogenic Markov Chains states including absorbent states, inessential and essential states, recurrent states and communicated states. We prove that if a state (i) according to a neutrosophic Markov Chain with neutrosophic transition matrix is classified as any of the previous classifications then it is also classified as the same classification in classical scene to two Markov Chains defined with transition matrices respectively. Also, we prove that if a state (i) according to a plithogenic Markov Chain with plithogenic tra

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13

Baumann, Hendrik, and Thomas Hanschke. "Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix." Journal of Applied Mathematics 2020 (July 8, 2020): 1–16. http://dx.doi.org/10.1155/2020/4318906.

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This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are exte

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14

Chen, Chun Hui, and Ya Fei Nie. "Algorithm and Implementation Write by R Software for Estimating the Transition Matrix of Homogeneous Markov Chain in Reliability Predictions." Advanced Materials Research 479-481 (February 2012): 971–76. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.971.

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Markov prediction is an important method predicts availability of repairable system. How to estimate the transition matrix and profit matrix (if it has) play a fundamental role in Markov prediction. This article introduced briefly homogeneous Markov chain prediction method, study on estimation and algorithm which calculate the transition matrix and profit matrix accompany with transition on the base of historical data about system state and profit. Finally, according to algorithm, we write a customized functions utilizing R software and provide the calling method more details. It did fundament

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15

Abdisa, Gemmechis Wendafiraw. "Modeling Earth Systems and Environment Land Use Land Cover Dynamics Using CA-Markov Chain Model and Geospatial Techniques: A Case of Belete Gera Regional Forest Priority Area, South Western Ethiopia." Forest Research: Open Access 12, no. 2 (2023): 12. https://doi.org/10.35248/2168-9776.23.12.340.

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Arrogant practices of land use including expansion of agricultural land and infrastructural development are resulting in deforestation that goes to climate change. Cellular Automata (CA)-Markov chain combines the advantages of cellular and Markov chain analysis to simulate and predict future land use/cover trends depending on the Land Use Land Cover (LULC) changes in the past. First, spatial distribution of LULC and area changed were calculated using IDRISI software and GIS technology, and then the forest land cover conversion to other LULC was evaluated to obtain rate of deforestation during

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16

Guerry, Marie-Anne. "On the Embedding Problem for Discrete-Time Markov Chains." Journal of Applied Probability 50, no. 4 (2013): 918–30. http://dx.doi.org/10.1239/jap/1389370090.

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When a discrete-time homogenous Markov chain is observed at time intervals that correspond to its time unit, then the transition probabilities of the chain can be estimated using known maximum likelihood estimators. In this paper we consider a situation when a Markov chain is observed on time intervals with length equal to twice the time unit of the Markov chain. The issue then arises of characterizing probability matrices whose square root(s) are also probability matrices. This characterization is referred to in the literature as the embedding problem for discrete time Markov chains. The prob

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Guerry, Marie-Anne. "On the Embedding Problem for Discrete-Time Markov Chains." Journal of Applied Probability 50, no. 04 (2013): 918–30. http://dx.doi.org/10.1017/s002190020001370x.

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When a discrete-time homogenous Markov chain is observed at time intervals that correspond to its time unit, then the transition probabilities of the chain can be estimated using known maximum likelihood estimators. In this paper we consider a situation when a Markov chain is observed on time intervals with length equal to twice the time unit of the Markov chain. The issue then arises of characterizing probability matrices whose square root(s) are also probability matrices. This characterization is referred to in the literature as the embedding problem for discrete time Markov chains. The prob

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18

Pritchard, Geoffrey, and David J. Scott. "The eigenvalues of the empirical transition matrix of a Markov chain." Journal of Applied Probability 41, A (2004): 347–60. http://dx.doi.org/10.1239/jap/1082552210.

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This paper investigates the probabilistic behaviour of the eigenvalue of the empirical transition matrix of a Markov chain which is of largest modulus other than 1, loosely called the second-largest eigenvalue. A central limit theorem is obtained for nonmultiple eigenvalues of the empirical transition matrix. When the Markov chain is actually a sequence of independent observations the distribution of the second-largest eigenvalue is determined and a test for independence is developed. The independence case is considered in more detail when the Markov chain has only two states, and some applica

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Pritchard, Geoffrey, and David J. Scott. "The eigenvalues of the empirical transition matrix of a Markov chain." Journal of Applied Probability 41, A (2004): 347–60. http://dx.doi.org/10.1017/s0021900200112409.

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This paper investigates the probabilistic behaviour of the eigenvalue of the empirical transition matrix of a Markov chain which is of largest modulus other than 1, loosely called the second-largest eigenvalue. A central limit theorem is obtained for nonmultiple eigenvalues of the empirical transition matrix. When the Markov chain is actually a sequence of independent observations the distribution of the second-largest eigenvalue is determined and a test for independence is developed. The independence case is considered in more detail when the Markov chain has only two states, and some applica

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20

Sherlaw-Johnson, Chris, Steve Gallivan, and Jim Burridge. "Estimating a Markov Transition Matrix from Observational Data." Journal of the Operational Research Society 46, no. 3 (1995): 405. http://dx.doi.org/10.2307/2584334.

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21

Sherlaw-Johnson, Chris, Steve Gallivan, and Jim Burridge. "Estimating a Markov Transition Matrix from Observational Data." Journal of the Operational Research Society 46, no. 3 (1995): 405–10. http://dx.doi.org/10.1057/jors.1995.55.

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22

Andradóttir, Sigrún, Daniel P. Heyman, and Teunis J. Ott. "Potentially unlimited variance reduction in importance sampling of Markov chains." Advances in Applied Probability 28, no. 1 (1996): 166–88. http://dx.doi.org/10.2307/1427916.

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We consider the application of importance sampling in steady-state simulations of finite Markov chains. We show that, for a large class of performance measures, there is a choice of the alternative transition matrix for which the ratio of the variance of the importance sampling estimator to the variance of the naive simulation estimator converges to zero as the sample path length goes to infinity. Obtaining this ‘optimal’ transition matrix involves computing the performance measure of interest, so the optimal matrix cannot be computed in precisely those situations where simulation is required

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23

Andradóttir, Sigrún, Daniel P. Heyman, and Teunis J. Ott. "Potentially unlimited variance reduction in importance sampling of Markov chains." Advances in Applied Probability 28, no. 01 (1996): 166–88. http://dx.doi.org/10.1017/s0001867800027312.

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We consider the application of importance sampling in steady-state simulations of finite Markov chains. We show that, for a large class of performance measures, there is a choice of the alternative transition matrix for which the ratio of the variance of the importance sampling estimator to the variance of the naive simulation estimator converges to zero as the sample path length goes to infinity. Obtaining this ‘optimal’ transition matrix involves computing the performance measure of interest, so the optimal matrix cannot be computed in precisely those situations where simulation is required

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24

Möhle, Martin, and Morihiro Notohara. "An extension of a convergence theorem for Markov chains arising in population genetics." Journal of Applied Probability 53, no. 3 (2016): 953–56. http://dx.doi.org/10.1017/jpr.2016.54.

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AbstractAn extension of a convergence theorem for sequences of Markov chains is derived. For every positive integer N let (XN(r))r be a Markov chain with the same finite state space S and transition matrix ΠN=I+dNBN, where I is the unit matrix, Q a generator matrix, (BN)N a sequence of matrices, limN℩∞cN= limN→∞dN=0 and limN→∞cN∕dN=0. Suppose that the limits P≔limm→∞(I+dNQ)m and G≔limN→∞PBNP exist. If the sequence of initial distributions PXN(0) converges weakly to some probability measure μ, then the finite-dimensional distributions of (XN([t∕cN))t≥0 converge to those of the Markov process (X

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25

Vassiliou, P. C. G. "Strong Ergodicity in Nonhomogeneous Markov Systems with Chronological Order." Mathematics 12, no. 5 (2024): 660. http://dx.doi.org/10.3390/math12050660.

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In the present, we study the problem of strong ergodicity in nonhomogeneous Markov systems. In the first basic theorem, we relax the fundamental assumption present in all studies of asymptotic behavior. That is, the assumption that the inherent inhomogeneous Markov chain converges to a homogeneous Markov chain with a regular transition probability matrix. In addition, we study the practically important problem of the rate of convergence to strong ergodicity for a nonhomogeneous Markov system (NHMS). In a second basic theorem, we provide conditions under which the rate of convergence to strong

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Shen, Hang, Zheng Nie, Jie Xia, and Qibin Wang. "A Markov method for a mechanical system reliability assessment using discrete degradation data." Journal of Physics: Conference Series 2815, no. 1 (2024): 012048. http://dx.doi.org/10.1088/1742-6596/2815/1/012048.

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Abstract A homogenous continuous-time Markov model (HCTMM) has the advantage of high accuracy and is usually used in reliability analysis. However, the transition intensities (rates) between any two states cannot be accurately obtained due to the discrete data obtained from a mechanical system and little expert knowledge. This paper proposes a method in which the transition intensity matrix of an HCTMM can be obtained indirectly using the actual discrete degradation data of a mechanical system. Firstly, the one-step transition probability matrix can be calculated by a hidden Markov model using

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Bäuerle, Nicole. "Monotonicity results for MR/GI/1 queues." Journal of Applied Probability 34, no. 2 (1997): 514–24. http://dx.doi.org/10.2307/3215390.

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This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.

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Bäuerle, Nicole. "Monotonicity results for MR/GI/1 queues." Journal of Applied Probability 34, no. 02 (1997): 514–24. http://dx.doi.org/10.1017/s0021900200101147.

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This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.

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Yap, V. B. "Similar States in Continuous-Time Markov Chains." Journal of Applied Probability 46, no. 2 (2009): 497–506. http://dx.doi.org/10.1239/jap/1245676102.

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In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models.

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Yap, V. B. "Similar States in Continuous-Time Markov Chains." Journal of Applied Probability 46, no. 02 (2009): 497–506. http://dx.doi.org/10.1017/s002190020000560x.

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In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models.

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Zhao, Yiqiang Q., Wei Li, and Attahiru Sule Alfa. "Duality results for block-structured transition matrices." Journal of Applied Probability 36, no. 4 (1999): 1045–57. http://dx.doi.org/10.1239/jap/1032374754.

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In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with r

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Zhao, Yiqiang Q., Wei Li, and Attahiru Sule Alfa. "Duality results for block-structured transition matrices." Journal of Applied Probability 36, no. 04 (1999): 1045–57. http://dx.doi.org/10.1017/s002190020001785x.

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In this paper, we consider a certain class of Markov renewal processes where the matrix of the transition kernel governing the Markov renewal process possesses some block-structured property, including repeating rows. Duality conditions and properties are obtained on two probabilistic measures which often play a key role in the analysis and computations of such a block-structured process. The method used here unifies two different concepts of duality. Applications of duality are also provided, including a characteristic theorem concerning recurrence and transience of a transition matrix with r

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Froyland, Gary, and Robyn M. Stuart. "Cheeger inequalities for absorbing Markov chains." Advances in Applied Probability 48, no. 3 (2016): 631–47. http://dx.doi.org/10.1017/apr.2016.20.

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Abstract We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain's conductance and metastability (and vice versa) with respect to its quasistationary distribution, extending classical results for stochastic transition matrices.

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Le, Hung V., and M. J. Tsatsomeros. "Matrix Analysis for Continuous-Time Markov Chains." Special Matrices 10, no. 1 (2021): 219–33. http://dx.doi.org/10.1515/spma-2021-0157.

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Abstract Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other stochastic properties. For the benefit of Perron-Frobenius cognoscentes, this theory is surveyed and further adapted to study continuous-time Markov chains on finite state spaces.

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Bonsdorff, Heikki. "On the Convergence Rate of Bonus-Malus Systems." ASTIN Bulletin 22, no. 2 (1992): 217–23. http://dx.doi.org/10.2143/ast.22.2.2005116.

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AbstractUnder certain conditions, a Bonus-Malus system can be interpreted as a Markov chain whose n-step transition probabilities converge to a limit probability distribution. In this paper, the rate of the convergence is studied by means of the eigenvalues of the transition probability matrix of the Markov chain.

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Malheiro, Elaís C., and Marcelo Viana. "Lyapunov exponents of linear cocycles over Markov shifts." Stochastics and Dynamics 15, no. 03 (2015): 1550020. http://dx.doi.org/10.1142/s0219493715500203.

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Esquível, Manuel L., Nadezhda P. Krasii, and Gracinda R. Guerreiro. "Open Markov Type Population Models: From Discrete to Continuous Time." Mathematics 9, no. 13 (2021): 1496. http://dx.doi.org/10.3390/math9131496.

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We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has opti

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Abolnikov, L., та A. Dukhovny. "Necessary and sufficient conditions for the ergodicity of Markov chains with transition Δm,n(Δ′m,n)-matrix". Journal of Applied Mathematics and Simulation 1, № 1 (1987): 13–24. http://dx.doi.org/10.1155/s1048953388000024.

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This paper isolates and studies a class of Markov chains with a special quasi-triangular form of the transition matrix [so-called Δm,n(Δ′m,n)-matrix]. Many discrete stochastic processes encountered in applications (queues, inventories and dams) have transition matrices which are special cases of a Δm,n(Δ′m,n)-matrix. Necessary and sufficient conditions for the ergodicity of a Markov chain with transition Δm,n(Δ′m,n)-matrix are determined in the article in two equivalent versions. According to the first version, these conditions are expressed in terms of certain restrictions imposed on the gene

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Fackeldey, Konstantin, Amir Niknejad, and Marcus Weber. "Finding metastabilities in reversible Markov chains based on incomplete sampling." Special Matrices 5, no. 1 (2017): 73–81. http://dx.doi.org/10.1515/spma-2017-0006.

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Abstract In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy,

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Bidabad, Bijan, and Behrouz Bidabad. "Complex Probability and Markov Stochastic Process." Indian Journal of Finance and Banking 3, no. 1 (2019): 13–22. http://dx.doi.org/10.46281/ijfb.v3i1.290.

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This note discusses the existence of "complex probability" in the real world sensible problems. By defining a measure more general than the conventional definition of probability, the transition probability matrix of discrete Markov chain is broken to the periods shorter than a complete step of the transition. In this regard, the complex probability is implied.

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de Carvalho, Walter A. F., Sandro Gallo, and Nancy L. Garcia. "Continuity properties of a factor of Markov chains." Journal of Applied Probability 53, no. 1 (2016): 216–30. http://dx.doi.org/10.1017/jpr.2015.20.

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Abstract Starting from a Markov chain with a finite or a countable infinite alphabet, we consider the chain obtained when all but one symbol are indistinguishable for the practitioner. We study conditions on the transition matrix of the Markov chain ensuring that the image chain has continuous or discontinuous transition probabilities with respect to the past.

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Coolen-Schrijner, Pauline, and Erik A. van Doorn. "THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN." Probability in the Engineering and Informational Sciences 16, no. 3 (2002): 351–66. http://dx.doi.org/10.1017/s0269964802163066.

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The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix Π is the matrix D ≡ ∫0∞(P(t) − Π) dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth–death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.

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Phatarfod, R. M., A. J. Pryde, and David Dyte. "On the move-to-front scheme with Markov dependent requests." Journal of Applied Probability 34, no. 3 (1997): 790–94. http://dx.doi.org/10.2307/3215104.

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In this paper we consider the operation of the move-to-front scheme where the requests form a Markov chain of N states with transition probability matrix P. It is shown that the configurations of items at successive requests form a Markov chain, and its transition probability matrix has eigenvalues that are the eigenvalues of all the principal submatrices of P except those of order N—1. We also show that the multiplicity of the eigenvalues of submatrices of order m is the number of derangements of N — m objects. The last result is shown to be true even if P is not a stochastic matrix.

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Phatarfod, R. M., A. J. Pryde, and David Dyte. "On the move-to-front scheme with Markov dependent requests." Journal of Applied Probability 34, no. 03 (1997): 790–94. http://dx.doi.org/10.1017/s0021900200101445.

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Abstract:

In this paper we consider the operation of the move-to-front scheme where the requests form a Markov chain of N states with transition probability matrix P . It is shown that the configurations of items at successive requests form a Markov chain, and its transition probability matrix has eigenvalues that are the eigenvalues of all the principal submatrices of P except those of order N—1. We also show that the multiplicity of the eigenvalues of submatrices of order m is the number of derangements of N — m objects. The last result is shown to be true even if P is not a stochastic matrix.

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Wu, Sheng-Jhih, and Moody T. Chu. "Constructing optimal transition matrix for Markov chain Monte Carlo." Linear Algebra and its Applications 487 (December 2015): 184–202. http://dx.doi.org/10.1016/j.laa.2015.09.016.

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Dukhovny, Alexander M. "Markov chains with quasitoeplitz transition matrix: first zero hitting." Journal of Applied Mathematics and Simulation 2, no. 3 (1989): 205–16. http://dx.doi.org/10.1155/s104895338900016x.

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This paper continues the investigation of Markov Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and mean times are found by the solution of special Riemann boundary value problems on the unit circle. Duality is discussed.

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Kang, Minsang, Eunkuk Son, Jinjae Lee, and Seungjin Kang. "Accurate Wind Speed Prediction Using Effective Markov Transition Matrix and Comparison with Other MCP Models." New & Renewable Energy 18, no. 1 (2022): 17–28. http://dx.doi.org/10.7849/ksnre.2022.0002.

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Hunter, Jeffrey J. "Markov chain properties in terms of column sums of the transition matrix." Acta et Commentationes Universitatis Tartuensis de Mathematica 16, no. 1 (2012): 33–51. http://dx.doi.org/10.12697/acutm.2012.16.03.

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Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the associated irreducible discrete time Markov chain. Some new relationships, including some inequalities, and partial answers to the questions, are given using a special generalized matrix inverse that has not previously been considered in the literature on Markov chains.

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Wibun, Anuchit, and Pipat Chaiwiwatworakul. "An Estimation of Thailand's Hourly Solar Radiation Using Markov Transition Matrix Method." Applied Mechanics and Materials 839 (June 2016): 29–33. http://dx.doi.org/10.4028/www.scientific.net/amm.839.29.

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To estimate global solar radiation from easy available weather forecast data (sky condition), Markov model is used for this estimation. The five-year (1996-2000) global radiation data that are taken at an hour intervals from Nakhon Pathom station, Thailand (latitude 13.81ºN and longitude 100.04ºE) are used to construct the Markov transition matrices. The global radiation sequences in 2000 will be generated by based on the characteristic probability of moving global radiation values which were observed from the obtained data during 1996-1999. The autocorrelation function is used for checking th

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Wang, Siwei. "Stock Price Prediction Based on Markov Chains." Highlights in Business, Economics and Management 23 (December 29, 2023): 1290–96. http://dx.doi.org/10.54097/27a01r65.

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Short-term trend prediction in the stock market is of significant importance for effective market regulation by the government and optimizing resource allocation for investors. It has become a research hotspot in both academia and the industry in recent years. In addressing the long-term stock price prediction problem, a Markov Chain-based stock price prediction method is proposed. This method is based on the concept of state transitions in Markov Chains, where stock indicator data is transformed into state data. A transition probability matrix is generated, and predictions are made using matr

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