On The Potential Problems Of Denumerable Markov Chain In Random Environment

This text is on the basis of mathematics model of Markov chain in random environment that Cogburn sets up, the several relevant problems potential of denumerable Markov chain in random environment are researched mainly.First of all, we discuss taboo probability of discrete Markov chain decomposition formulas basically in random environment, and introduce the concept that the state can be reached under the condition of the taboo set, a result of the moments of fist entrance time distributions is given. Moreover, provide the concepts of random harmonic functions, extreme harmonic function and inevitable exit set, some basic properties of them are studied by the concepts of inevitable exit sets, and then a sufficient condition for random harmonic functions to be the constant vector functions is obtained. Finally, the potential of denumerable Markov chain in random environment is preliminary that we have studied. Introduce the concept of random regular function and random potential function at first, a necessary and sufficient condition of random potential function for denumerable Markov chain in random environment is provided, and the unique decomposition property of nonnegative random super-regular function is discussed.