The construction of denumerable q-processes in random environments satisfying (F) or (B)

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.