Entrance and Sojourn Times for Markov Chains. Application to $\boldsymbol{(L,R)}$-random walks

#### V. Cammarota, A. Lachal

2015, v.21, Issue 4, 887-938

ABSTRACT

In this paper, we provide a methodology for computing the probability
distribution of sojourn times for a wide class of Markov chains. Our methodology
consists in writing out linear systems and matrix equations for generating
functions involving relations with entrance times.
We apply the developed methodology to some classes of random walks with
bounded integer-valued jumps.

Keywords: sojourn times, Entrance times, $(L,R)$-random walks, Generating functions, Matrix equations