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,p —m 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 byp —m 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.