Abstract:

This article is a continuation of [9]. Based on the discussion of random Kolmogorov forward (backward) equations, for any given q-matrix in random environment, Q(θ)=(q(θ; x, y), x, y∈ χ), an infinite class of q-processes in random environments satisfying the random Kolmogorov forward (backward) equation is constructed. Moreover, under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed.

Key words: Markov process in random environment, q-matrix in random environment,
q-process in random environment