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Books on the topic 'Continuous time Markov chain'

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Published: 4 June 2021
Last updated: 11 June 2025

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1

Anderson, William J. Continuous-Time Markov Chains. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-3038-0.

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2

Yin, G. George, and Qing Zhang. Continuous-Time Markov Chains and Applications. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0627-9.

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3

Yin, G. George, and Qing Zhang. Continuous-Time Markov Chains and Applications. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4346-9.

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4

J, Anderson William. Continuous-time Markov chains: An applications-oriented approach. Springer-Verlag, 1991.

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5

J, Anderson William. Continuous-time Markov chains: An applications-oriented approach. Springer-Verlag, 1991.

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6

Yin, George. Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach. 2nd ed. Springer New York, 2013.

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7

Yin, George. Continuous-time Markov chains and applications: A singular perturbation approach. Springer, 1998.

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8

Yin, G. George. Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. Springer New York, 1998.

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9

Guo, Xianping, and Onésimo Hernández-Lerma. Continuous-Time Markov Decision Processes. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02547-1.

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10

Piunovskiy, Alexey, and Yi Zhang. Continuous-Time Markov Decision Processes. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54987-9.

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11

Costa, Oswaldo L. V., Marcelo D. Fragoso, and Marcos G. Todorov. Continuous-Time Markov Jump Linear Systems. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-34100-7.

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12

Costa, Oswaldo L. V. Continuous-Time Markov Jump Linear Systems. Springer Berlin Heidelberg, 2013.

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13

Continuous time Markov processes: An introduction. American Mathematical Society, 2010.

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14

Liggett, Thomas M. Continuous time Markov processes: An introduction. American Mathematical Society, 2010.

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15

Fragoso, Marcelo D. Continuous-time Markov jump linear systems. Springer, 2013.

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16

Hernández-Lerma, O. Lectures on continuous-time Markov control processes. Sociedad Matemática Mexicana, 1994.

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17

Banjevic, Dragan. Recurrent relations for distribution of waiting time in Markov chain. University of Toronto, Department of Statistics, 1994.

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18

Roberts, Gareth O. Quantitative bounds for convergence rates of continuous time Markov processes. University of Toronto, Dept. of Statistics, 1996.

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19

Kushner, Harold J. Numerical methods for stochastic control problems in continuous time. Springer-Verlag, 1992.

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20

Kushner, Harold J. Numerical methods for stochastic control problems in continuous time. 2nd ed. Springer, 2001.

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21

Mathematics of probability. American Mathematical Society, 2013.

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22

Vladas, Sidoravicius, and Smirnov S. (Stanislav) 1970-, eds. Probability and statistical physics in St. Petersburg: St. Petersburg School in Probability and Statistical Physics : June 18-29, 2012 : St. Petersburg State University, St. Petersburg, Russia. American Mathematical Society, 2015.

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23

J, Anderson William. Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, 2014.

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24

J, Anderson William. Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer, 2011.

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25

J, Anderson William. Continuous-Time Markov Chains: An Applications-Oriented Approach. Springer London, Limited, 2012.

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26

Zhang, Qing, and G. George Yin. Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach. Springer New York, 2014.

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27

Zhang, Qing, and G. George Yin. Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach. Springer, 2012.

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28

Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach. Springer, 2011.

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29

Zhang, Qing, and George G. Yin. Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach (Stochastic Modelling and Applied Probability). Springer, 1997.

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30

Back, Kerry E. Learning. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0023.

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Continuous‐time filtering is explained, including the Kalman filter and filtering for a Markov chain with hidden states. Filtering theory is applied to analyze portfolio choice and equilibrium asset prices. When the expected return of an asset is unknown and is estimated from past returns, the myopic demand is a momentum strategy. When investors learn expected consumption growth from realized consumption growth, equilibrium prices are more sensitive to consumption shocks and the equity premium is higher. When the consumption growth rate follows a Markov chain with hidden states, return volatility tends to be higher when investors are less certain about which state the economy is in.
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31

Oswaldo Luiz do Valle Costa, Marcelo D. Fragoso, and Marcos G. Todorov. Continuous-Time Markov Jump Linear Systems. Springer, 2015.

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32

Oswaldo Luiz do Valle Costa, Marcelo D. Fragoso, and Marcos G. Todorov. Continuous-Time Markov Jump Linear Systems. Springer, 2012.

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33

Hernandez-Lerma, Onesimo, and Xianping Guo. Continuous-Time Markov Decision Processes: Theory and Applications. Springer, 2010.

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34

Hernández-Lerma, Onésimo, and Xianping Guo. Continuous-Time Markov Decision Processes: Theory and Applications. Springer, 2012.

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35

Kushner, Harold J., and Paul Dupuis. Numerical Methods for Stochastic Control Problems in Continuous Time. Springer, 2013.

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36

Back, Kerry E. Continuous-Time Markets. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0013.

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A continuous‐time model of a securities market is introduced. The intertemporal budget constraint is defined. SDF processes and prices of risks are defined and characterized. Many properties of SDF process are analogous to those in a single‐period model, including the relation to the risk‐free rate, orthogonal projections, the Hansen‐Jagannathan bound, and factor pricing. To value future cash flows using an SDF process, we need to assume a local martingale is a martingale. Sufficient conditions including Novikov’s condition are discussed. Use of the martingale representation theorem in a complete market to derive a portfolio that replicates a payoff is explained. A Markovian model is introduced, in which the investment opportunity set depends on state variables that form a Markov process.
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37

Zhang, Yi, Alexey Piunovskiy, and Albert Nikolaevich Shiryaev. Continuous-Time Markov Decision Processes: Borel Space Models and General Control Strategies. Springer International Publishing AG, 2021.

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38

Zhang, Yi, Alexey Piunovskiy, and Albert Nikolaevich Shiryaev. Continuous-Time Markov Decision Processes: Borel Space Models and General Control Strategies. Springer International Publishing AG, 2020.

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39

Bosch, Mariano, and William Maloney. Labor Market Dynamics In Developing Countries: Comparative Analysis Using Continuous Time Markov Processes. The World Bank, 2005. http://dx.doi.org/10.1596/1813-9450-3583.

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40

Hernandez-Lerma, Onesimo, and Xianping Guo. Continuous-Time Markov Decision Processes: Theory and Applications (Stochastic Modelling and Applied Probability Book 62). Springer, 2009.

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41

Bao, Yun, Carl Chiarella, and Boda Kang. Particle Filters for Markov-Switching Stochastic Volatility Models. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.9.

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This chapter proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. It proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method that demonstrates the ability to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is implemented in order to analyze a real-time series, namely, the foreign exchange rate between the Australian dollar and the South Korean won.
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42

Boudreau, Joseph F., and Eric S. Swanson. Monte Carlo methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0007.

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Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use in for sampling a variety of nonuniform distributions, for both continuous and discrete variables. A wide selection of uniform and nonuniform variate generators from the C++ standard library are reviewed, and common techniques for generating custom nonuniform variates are discussed. The chapter presents the uses of Monte Carlo to evaluate integrals, particularly multidimensional integrals, and then introduces the important method of Markov chain Monte Carlo, suitable for solving a wide range of scientific problems that require the sampling of complicated multivariate distributions. Relevant topics in probability and statistics are also introduced in this chapter. Finally, the topics of thermalization, autocorrelation, multimodality, and Gibbs sampling are presented.
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43

Geweke, John, Gary Koop, and Herman Van Dijk, eds. The Oxford Handbook of Bayesian Econometrics. Oxford University Press, 2011. http://dx.doi.org/10.1093/oxfordhb/9780199559084.001.0001.

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Bayesian econometric methods have enjoyed an increase in popularity in recent years. Econometricians, empirical economists, and policymakers are increasingly making use of Bayesian methods. The Oxford Handbook of Bayesian Econometrics is a single source about Bayesian methods in specialized fields. It contains articles by leading Bayesians on the latest developments in their specific fields of expertise. The volume provides broad coverage of the application of Bayesian econometrics in the major fields of economics and related disciplines, including macroeconomics, microeconomics, finance, and marketing. It reviews the state of the art in Bayesian econometric methodology, with articles on posterior simulation and Markov chain Monte Carlo methods, Bayesian nonparametric techniques, and the specialized tools used by Bayesian time series econometricians such as state space models and particle filtering. It also includes articles on Bayesian principles and methodology.
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44

Henderson, Daniel A., R. J. Boys, Carole J. Proctor, and Darren J. Wilkinson. Linking systems biology models to data: A stochastic kinetic model of p53 oscillations. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.7.

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This article discusses the use of a stochastic kinetic model to study protein level oscillations in single living cancer cells, using the p53 and Mdm2 proteins as examples. It describes the refinement of a dynamic stochastic process model of the cellular response to DNA damage and compares this model to time course data on the levels of p53 and Mdm2. The article first provides a biological background on p53 and Mdm2 before explaining how the stochastic kinetic model is constructed. It then introduces the stochastic kinetic model and links it to the data and goes on to apply sophisticated MCMC methods to compute posterior distributions. The results demonstrate that it is possible to develop computationally intensive Markov chain Monte Carlo (MCMC) methods for conducting a Bayesian analysis of an intra-cellular stochastic systems biology model using single-cell time course data.
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45

Quintana, José Mario, Carlos Carvalho, James Scott, and Thomas Costigliola. Extracting S&P500 and NASDAQ Volatility: The Credit Crisis of 2007–2008. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.13.

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This article demonstrates the utility of Bayesian modelling and inference in financial market volatility analysis, using the 2007-2008 credit crisis as a case study. It first describes the applied problem and goal of the Bayesian analysis before introducing the sequential estimation models. It then discusses the simulation-based methodology for inference, including Markov chain Monte Carlo (MCMC) and particle filtering methods for filtering and parameter learning. In the study, Bayesian sequential model choice techniques are used to estimate volatility and volatility dynamics for daily data for the year 2007 for three market indices: the Standard and Poor’s S&P500, the NASDAQ NDX100 and the financial equity index called XLF. Three models of financial time series are estimated: a model with stochastic volatility, a model with stochastic volatility that also incorporates jumps in volatility, and a Garch model.
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46

Martin, Andrew D. Bayesian Analysis. Edited by Janet M. Box-Steffensmeier, Henry E. Brady, and David Collier. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199286546.003.0021.

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This article surveys modern Bayesian methods of estimating statistical models. It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown. The article finally provides a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science. One area ripe for research is the use of prior information in statistical analyses. Mixture models and those with discrete parameters (such as change point models in the time-series context) are completely underutilized in political science.
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47

Delsol, Laurent. Nonparametric Methods for α-Mixing Functional Random Variables. Редактори Frédéric Ferraty та Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.5.

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This article considers how functional kernel methods can be used to study α-mixing datasets. It first provides an overview of how prediction problems involving dependent functional datasets may arise from the study of time series, focusing on the standard discretized model and modelization that takes into account the functional nature of the evolution of the quantity to be studied over time. It then considers strong mixing conditions, with emphasis on the notion of α-mixing coefficients and α-mixing variables introduced by Rosenblatt (1956). It also describes some conditions for a Markov chain to be α-mixing; some useful tools that provide covariance inequalities, exponential inequalities, and Central Limit Theorem (CLT) for α-mixing sequences; the asymptotic properties of functional kernel estimators; the use of kernel smoothing methods with α-mixing datasets; and various functional kernel estimators corresponding to different prediction methods. Finally, the article highlights some interesting prospects for further research.
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48

Laver, Michael, and Ernest Sergenti. Systematically Interrogating Agent-Based Models. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691139036.003.0004.

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This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the different methods of experimental design, such as grid sweeping and Monte Carlo parameterization. Next, it demonstrates how to calculate mean estimates of output variables of interest. It does so by first discussing stochastic processes, Markov Chain representations, and model burn-in. It focuses on three stochastic process representations: nonergodic deterministic processes that converge on a single state; nondeterministic stochastic processes for which a time average provides a representative estimate of the output variables; and nondeterministic stochastic processes for which a time average does not provide a representative estimate of the output variables. The estimation strategy employed depends on which stochastic process the simulation follows. Lastly, the chapter presents a set of diagnostic checks used to establish an appropriate sample size for the estimation of the means.
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