@TechReport{ it:2006-033,
author = {Parosh Aziz Abdulla and Noomene Ben Henda and Richard Mayr
and Sven Sandberg},
title = {Limiting Behavior of {M}arkov Chains with Eager
Attractors},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Computer Systems},
year = {2006},
number = {2006-033},
month = jun,
abstract = {We consider discrete infinite-state Markov chains which
contain an eager finite attractor. A finite attractor is a
finite subset of states that is eventually reached with
probability 1 from every other state, and the eagerness
condition requires that the probability of avoiding the
attractor in $n$ or more steps after leaving it is
exponentially bounded in $n$. Examples of such Markov
chains are those induced by probabilistic lossy channel
systems and similar systems. We show that the expected
residence time (a generalization of the steady state
distribution) exists for Markov chains with eager
attractors and that it can be effectively approximated to
arbitrary precision. Furthermore, arbitrarily close
approximations of the limiting average expected reward,
with respect to state-based bounded reward functions, are
also computable. }
}