Abstract
In this note we study the probability and the
mean time for absorption for discrete time Markov chains. In particular, we are
interested in estimating the mean time for absorption when
absorption is not certain and connect it with some other known
results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets
A
1
,
A
2
,
…
,
A
k
{A_{1},A_{2},\dots,A_{k}}
.
The strong deviation theorem for discrete-time and continuous-state nonhomogeneous Markov chains
