Random evolutions processes induced by discrete time Markov chains.
Keepler, M. (1998)
Portugaliae Mathematica
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Keepler, M. (1998)
Portugaliae Mathematica
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Stephen J. Kirkland (2016)
Czechoslovak Mathematical Journal
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We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny's constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time...
Mariusz Górajski (2009)
Annales UMCS, Mathematica
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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...
Alexei Borodin (2008)
Annales de l'I.H.P. Probabilités et statistiques
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We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Persi Diaconis, Steven N. Evans (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Bogolyubov, N.M. (2005)
Zapiski Nauchnykh Seminarov POMI
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Russell Lyons, Yuval Peres, Oded Schramm (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Z. Porosiński (1988)
Applicationes Mathematicae
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Ryszard Rudnicki (2000)
Applicationes Mathematicae
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This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.