Abstract
The concepts of Markov process in random environment,q-matrix in random environment andq-process in random environment are introduced. Three forms of random Kolmoogrov farward (or backward) equations are introduced and the equivalence of these three forms are also proved. Moreover any conservativeq-process in random environment satisfies random Kolmogrov backward equation.
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References
Nawrotzki K. Discrete Open System of Markov Chains in a Random Environment, I; II.J Inform Process Cybernet, 1981,17: 569–599; 1982,18: 83–98.
Cogburn R. Markov Chains in Random Environments, the Case of Markovian Environments.Ann Probab, 1980,8: 908–916.
Cogburn R. The Ergodic Theory of Markov Chains in Random Environments.Z Wahrach View Gebiete, 1984,66: 109–128.
Cogburn R. On Direct Convergence and Periodicity for Transition Probailities of Markov Chains in Random environments.Ann Probab, 1990,18: 642–654.
Cogburn R. On the Central Limit Theorem for Markov Chains in Random Enivronments.Ann Probab, 1991,19: 587–604.
Kifer Y. Limit Theorems for Random Transformations and Processes in Random Environmens.Tran Amer Math Soci, 1998,350: 1481–1518.
Orey S. Markov Chains with Stochastically Stationary Transition Probabilities.Ann Probab, 1991,19: 907–928.
eu D H. The Construction of Markov Processes in Random Environments and Equivalence Theorems.Science in China (Series A), 2004,34: 268–282.
Hu D H. The Existence and Uniqueness ofq-Process in Random Environment.Science in China (Series A), 2004,34: 641–658.
Hu D H.Stochastic Processes-Basis, Theory and Applications (Second Edition). Wuhan: Wuhan University Press, 2002, 379(Ch).
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Foundation item: Supported by the National Natural Science Foundation of China (10371092 and 10171102) and the Foundation of Wuhan University.
Biography: HU Di-he(1935-), male, Professor, research direction: stochastic processes and random fractals.
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Di-he, H., Xiao-yu, H. The equivalence forms of random Kolmogorov forward(backward) equations. Wuhan Univ. J. Nat. Sci. 10, 808–812 (2005). https://doi.org/10.1007/BF02832417
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DOI: https://doi.org/10.1007/BF02832417