Abstract:

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient
conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

Key words: Markov process in random environment, random transition function, homogeneous random transition function, random Kolmogorov backward equation, random Kolmogorov forward equation