# Reduction of absorbing Markov chain

Annales UMCS, Mathematica (2009)

- Volume: 63, Issue: 1, page 91-107
- ISSN: 2083-7402

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topMariusz Górajski. "Reduction of absorbing Markov chain." Annales UMCS, Mathematica 63.1 (2009): 91-107. <http://eudml.org/doc/267705>.

@article{MariuszGórajski2009,

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 nondecreasing sequence of stopping times. Random walk on the initial Markov chain observed exclusively in the stopping times τ1, τ2, … is equivalent to some new Markov chain.},

author = {Mariusz Górajski},

journal = {Annales UMCS, Mathematica},

keywords = {Absorbing Markov chain; distribution of time to absorption; absorbing Markov chain},

language = {eng},

number = {1},

pages = {91-107},

title = {Reduction of absorbing Markov chain},

url = {http://eudml.org/doc/267705},

volume = {63},

year = {2009},

}

TY - JOUR

AU - Mariusz Górajski

TI - Reduction of absorbing Markov chain

JO - Annales UMCS, Mathematica

PY - 2009

VL - 63

IS - 1

SP - 91

EP - 107

AB - 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 nondecreasing sequence of stopping times. Random walk on the initial Markov chain observed exclusively in the stopping times τ1, τ2, … is equivalent to some new Markov chain.

LA - eng

KW - Absorbing Markov chain; distribution of time to absorption; absorbing Markov chain

UR - http://eudml.org/doc/267705

ER -

## References

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