@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. }
}