On the completeness of Markovian plans of discrete-time random walks with sparse matrix of transition probabilities (Q5942240)

In correspondence with a Markovian random walk plan \(\Pi(\pi,G)\) a homogeneous Markov chain \(\xi_t\), \(t= 0,1,\dots\), is observed with initial distribution \(\pi= (1,0,\dots, 0)\) and unknown transition matrix \(\Theta= \|\theta_{ij}\|^k_1\), \(G\) is the stopping boundary. The paper presents conditions under which this plan of walks is complete if \(\Theta\) is taken from the set of regular stochastic matrices \(\Theta_A\) satisfying some further conditions. Two examples illustrate the obtained results.