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2009 | 63 | 1 | 91-107
Tytuł artykułu

Reduction of absorbing Markov chain

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
63
Numer
1
Strony
91-107
Opis fizyczny
Daty
wydano
2009-01-01
online
2010-01-22
Twórcy
  • The Faculty of Mathematics and Computer Science, University of Łódź, ul. Stefana Banacha 22 90-238 Łódź Poland
Bibliografia
  • Billingsley, P., Probability and Measure, John Wiley & Sons, New York, 1979.
  • Chandrasekharan, M. P., Madhusudanan Pillai, V., An absorbing Markov chain model for production systems with rework and scrapping, Computers and Industrial Engineering 55, Issue 3 (2008), 695-706.
  • Engel, A., The probabilistic abacus, Educational Studies in Mathematics 6 (1975), 1-22.
  • Engel, A., Why does the probabilistic abacus work?, Educational Studies in Mathematics 7 (1976), 59-56.
  • Feller, W., An Introduction to Probability Theory and Its Applications, John Wiley & Sons, New York, 1968.
  • Gosselin, F., Asymptotic behavior of absorbing Markov chains conditional on nonabsorption for application in conservation biology, Ann. Appl. Probab. 11, no. 1 (2001), 261-284.
  • Iosifescu, M., Finite Markov Processes and Their Applications, John Wiley & Sons, Chichester, 1980.
  • Kemeny, J. G., Snell, J. L., Finite Markov Chain, D. Van Nostrand, Princeton, 1960.
  • Keming Gu, Sadiku, M. N. O., Absorbing Markov chain solution for Possion's equation, Southeastcon 2000. Proceedings of the IEEE (2000), 297-300.
  • Norris, J. R., Markov Chain, Cambridge University Press, Cambridge, 1997.
  • Płocki, A., Introduction to probability calculus and mathematical statistics for teachers, Propedeutyka rachunku prawdopodobieństwa i statystyki matematycznej dla nauczycieli, PWN, Warszawa 1992 (Polish).
  • Swan, Y. C., Bruss, F. T., A matrix-analytic approach to the N-player ruin problem, J. Appl. Probab. 43, no. 3 (2006), 755-766.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10062-009-0009-7
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