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Relevant bibliographies by topics / Markov reversibility

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Journal articles

Academic literature on the topic 'Markov reversibility'

Author: Grafiati

Published: 23 September 2022

Last updated: 21 October 2022

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Journal articles on the topic "Markov reversibility"

1

Beare, Brendan K., and Juwon Seo. "TIME IRREVERSIBLE COPULA-BASED MARKOV MODELS." Econometric Theory 30, no. 5 (2014): 923–60. http://dx.doi.org/10.1017/s0266466614000115.

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Economic and financial time series frequently exhibit time irreversible dynamics. For instance, there is considerable evidence of asymmetric fluctuations in many macroeconomic and financial variables, and certain game theoretic models of price determination predict asymmetric cycles in price series. In this paper, we make two primary contributions to the econometric literature on time reversibility. First, we propose a new test of time reversibility, applicable to stationary Markov chains. Compared to existing tests, our test has the advantage of being consistent against arbitrary violations of reversibility. Second, we explain how a circulation density function may be used to characterize the nature of time irreversibility when it is present. We propose a copula-based estimator of the circulation density and verify that it is well behaved asymptotically under suitable regularity conditions. We illustrate the use of our time reversibility test and circulation density estimator by applying them to five years of Canadian gasoline price markup data.

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2

Ōsawa, Hideo. "Reversibility of Markov chains with applications to storage models." Journal of Applied Probability 22, no. 1 (1985): 123–37. http://dx.doi.org/10.2307/3213752.

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This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

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3

Ōsawa, Hideo. "Reversibility of Markov chains with applications to storage models." Journal of Applied Probability 22, no. 01 (1985): 123–37. http://dx.doi.org/10.1017/s0021900200029053.

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Abstract:

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

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4

Steuber, Tara L., Peter C. Kiessler, and Robert Lund. "TESTING FOR REVERSIBILITY IN MARKOV CHAIN DATA." Probability in the Engineering and Informational Sciences 26, no. 4 (2012): 593–611. http://dx.doi.org/10.1017/s0269964812000228.

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This paper introduces two statistics that assess whether (or not) a sequence sampled from a stationary time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.

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5

Kämpke, T. "Reversibility and equivalence in directed markov fields." Mathematical and Computer Modelling 23, no. 3 (1996): 87–101. http://dx.doi.org/10.1016/0895-7177(95)00235-9.

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6

Ge, Hao, Da-Quan Jiang, and Min Qian. "Reversibility and entropy production of inhomogeneous Markov chains." Journal of Applied Probability 43, no. 04 (2006): 1028–43. http://dx.doi.org/10.1017/s0021900200002400.

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In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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7

Ge, Hao, Da-Quan Jiang, and Min Qian. "Reversibility and entropy production of inhomogeneous Markov chains." Journal of Applied Probability 43, no. 4 (2006): 1028–43. http://dx.doi.org/10.1239/jap/1165505205.

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In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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8

Tetali, Prasad. "An Extension of Foster's Network Theorem." Combinatorics, Probability and Computing 3, no. 3 (1994): 421–27. http://dx.doi.org/10.1017/s0963548300001309.

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Consider an electrical network onnnodes with resistorsrijbetween nodesiandj. LetRijdenote theeffective resistancebetween the nodes. Then Foster's Theorem [5] asserts thatwherei∼jdenotesiandjare connected by a finiterij. In [10] this theorem is proved by making use of random walks. The classical connection between electrical networks and reversible random walks implies a corresponding statement for reversible Markov chains. In this paper we prove an elementary identity for ergodic Markov chains, and show that this yields Foster's theorem when the chain is time-reversible.We also prove a generalization of aresistive inverseidentity. This identity was known for resistive networks, but we prove a more general identity for ergodic Markov chains. We show that time-reversibility, once again, yields the known identity. Among other results, this identity also yields an alternative characterization of reversibility of Markov chains (see Remarks 1 and 2 below). This characterization, when interpreted in terms of electrical currents, implies thereciprocity theoremin single-source resistive networks, thus allowing us to establish the equivalence ofreversibilityin Markov chains andreciprocityin electrical networks.

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9

Serfozo, Richard F. "Reversible Markov processes on general spaces and spatial migration processes." Advances in Applied Probability 37, no. 03 (2005): 801–18. http://dx.doi.org/10.1017/s0001867800000483.

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In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

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10

Serfozo, Richard F. "Reversible Markov processes on general spaces and spatial migration processes." Advances in Applied Probability 37, no. 3 (2005): 801–18. http://dx.doi.org/10.1239/aap/1127483748.

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Abstract:

In this study, we characterize the equilibrium behavior of spatial migration processes that represent population migrations, or birth-death processes, in general spaces. These processes are reversible Markov jump processes on measure spaces. As a precursor, we present fundamental properties of reversible Markov jump processes on general spaces. A major result is a canonical formula for the stationary distribution of a reversible process. This involves the characterization of two-way communication in transitions, using certain Radon-Nikodým derivatives. Other results concern a Kolmogorov criterion for reversibility, time reversibility, and several methods of constructing or identifying reversible processes.

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