Asymptotic behaviour of transition probability of uniform Markovian process with the finite number of states in the scheme of series

Abstract

The asymptotic behavior of the transition probabilities P_ij ⁽ⁿ⁾(t/ɛ_n) for a homogeneous stochastically continuous Markov process with a finite set of states E where E can be represented in the form виде E = E₀UE₁U…UE_r, E₀ is the set of unessential states, E_k, k=1, ..., r are ergodic classes.