Abstract
In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a non- decreasing sequence of stopping times. Random walk on the initial Markov chain observed exclusively in the stopping times 1; 2;::: is equivalent to some new Markov chain.
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