Science in China Series A: Mathematics

, Volume 47, Issue 4, pp 481–496 | Cite as

The construction of markov processes in random environments and the equivalence theorems



In sec.1, we introduce several basic concepts such as random transition function,pm process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec. 2, we construct the Markov process in random enviromment and skew product Markov process bypm process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.


radom transition function pm process Markov process in random environment skew product Markov process density function 


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  1. 1.
    Nawrotzki, K., Discrete open system of Markov chains in a random environment, I, II, J. Inform. Process, Cybernet, Cybernet, 1981, 17: 569–599, 1982, 18: 83-98.zbMATHMathSciNetGoogle Scholar
  2. 2.
    Cogburn, R., Markov chains in random environments, The case of Markovian environments, Ann. Probab., 1980, 8: 908–916.zbMATHMathSciNetGoogle Scholar
  3. 3.
    Cogburn, R., The ergodic theory of Markov chains in random environments, Z. Wahrach. Verw, Gebiete., 1984, 66: 109–128.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cogburn, R., On direct convergence and periodicity for transition probabilities of Markov chains in random environments, Ann. Probab., 1990, 18: 642–654.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cogburn, R., On the central limit theorem for Markov chains in random environments, Ann. Probab., 1991, 19: 587–604.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Orey, S., Markov chains with stochastically stationary transition probabilities, Ann. probab., 1991, 19: 907–928.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kiefer, Y., Limit theorems for random transformations and processes in random environments, Tran. Amer. Math. Soci., 1998, 350: 1481–1518.CrossRefGoogle Scholar
  8. 8.
    Li, Y., The recurrence and invariant measures for Markov chains in bi-infinite environments, Science in China, Ser. A, 2001, 31: 702–707.Google Scholar
  9. 9.
    Hu, D., Stochastic Processes, Basis, Theory and Applications, Wuhan: Wuhan University Press, 2000.Google Scholar
  10. 10.
    Chung, K. L., Markov chains with stationary transition probabilities, 2nd ed., New York: Springer-Verlag, 1967.zbMATHGoogle Scholar
  11. 11.
    Hu, D., Theory of Denumerable Markov Processes (in Chinese), Wuhan: Wuhan University Press, 1983.Google Scholar
  12. 12.
    Hu, D., The Limit Distribution of Functional for Markov Chains (in Chinese), Wuhan University Bulletin, 1977, 3: 63–79.Google Scholar

Copyright information

© Science in China press 2004

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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