Number of successes in Markov trials

U. Narayan Bhat; Ram Lal

doi:10.2307/1427041

Number of successes in Markov trials

Advances in Applied Probability ◽

10.1017/s0001867800018206 ◽

1988 ◽

Vol 20 (03) ◽

pp. 677-680 ◽

Cited By ~ 2

Author(s):

U. Narayan Bhat ◽

Ram Lal

Keyword(s):

Markov Chain ◽

Markov Chain Model ◽

First Passage Time ◽

Passage Time ◽

Chain Model ◽

First Passage

Markov trials are a sequence of dependent trials with two outcomes, success and failure, which are the states of a Markov chain. The distribution of the number of successes in n Markov trials and the first-passage time for a specified number of successes are obtained using an augmented Markov chain model.

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Mapping absorption processes onto a Markov chain, conserving the mean first passage time

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/46/14/145001 ◽

2013 ◽

Vol 46 (14) ◽

pp. 145001 ◽

Cited By ~ 1

Author(s):

Katja Biswas

Keyword(s):

Markov Chain ◽

First Passage Time ◽

Passage Time ◽

Mean First Passage Time ◽

First Passage ◽

The Mean

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First passage time Markov chain analysis of rare events for kinetic Monte Carlo: double kink nucleation during dislocation glide

Modelling and Simulation in Materials Science and Engineering ◽

10.1088/0965-0393/10/5/308 ◽

2002 ◽

Vol 10 (5) ◽

pp. 581-596 ◽

Cited By ~ 22

Author(s):

C S Deo ◽

D J Srolovitz

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Kinetic Monte Carlo ◽

First Passage Time ◽

Passage Time ◽

Markov Chain Analysis ◽

First Passage ◽

Dislocation Glide ◽

Double Kink ◽

Chain Analysis

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On passage and conditional passage times for Markov chains in continuous time

Journal of Applied Probability ◽

10.1017/s0021900200040924 ◽

1988 ◽

Vol 25 (02) ◽

pp. 279-290 ◽

Cited By ~ 1

Author(s):

Masaaki Kijima

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Continuous Time ◽

First Passage Time ◽

Passage Time ◽

Death Process ◽

First Passage ◽

Reversible Markov Chain ◽

Irreducible Markov Chain ◽

Passage Times

Let X(t) be a temporally homogeneous irreducible Markov chain in continuous time defined on . For k < i < j, let H = {k + 1, ···, j − 1} and let kTij ( jTik ) be the upward (downward) conditional first-passage time of X(t) from i to j(k) given no visit to . These conditional passage times are studied through first-passage times of a modified chain HX(t) constructed by making the set of states absorbing. It will be shown that the densities of kTij and jTik for any birth-death process are unimodal and the modes kmij ( jmik ) of the unimodal densities are non-increasing (non-decreasing) with respect to i. Some distribution properties of kTij and jTik for a time-reversible Markov chain are presented. Symmetry among kTij, jTik , and is also discussed, where , and are conditional passage times of the reversed process of X(t).

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First Passage Time of a Markov Chain That Converges to Bessel Process

Abstract and Applied Analysis ◽

10.1155/2017/7189826 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Moussa Kounta

Keyword(s):

Markov Chain ◽

First Passage Time ◽

Passage Time ◽

Bessel Process ◽

Hitting Time ◽

The Other ◽

First Hitting Time ◽

First Passage ◽

Discrete Markov Chain

We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process.

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Minimising the largest mean first passage time of a Markov chain: The influence of directed graphs

Linear Algebra and its Applications ◽

10.1016/j.laa.2017.01.034 ◽

2017 ◽

Vol 520 ◽

pp. 306-334

Author(s):

Jane Breen ◽

Steve Kirkland

Keyword(s):

Markov Chain ◽

First Passage Time ◽

Directed Graphs ◽

Passage Time ◽

Mean First Passage Time ◽

First Passage

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Using the First Passage Times in Markov Chain Model to Support Financial Decisions on the Stock Exchange

Dynamic Econometric Models ◽

10.12775/dem.2016.003 ◽

2016 ◽

Vol 16 (1) ◽

pp. 37

Author(s):

Józef Stawicki

Keyword(s):

Markov Chain ◽

Stock Exchange ◽

Markov Chain Model ◽

First Passage Times ◽

Chain Model ◽

First Passage ◽

Financial Decisions ◽

Passage Times

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On passage and conditional passage times for Markov chains in continuous time

Journal of Applied Probability ◽

10.2307/3214436 ◽

1988 ◽

Vol 25 (2) ◽

pp. 279-290 ◽

Cited By ~ 3

Author(s):

Masaaki Kijima

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Continuous Time ◽

First Passage Time ◽

Passage Time ◽

Death Process ◽

First Passage ◽

Reversible Markov Chain ◽

Irreducible Markov Chain ◽

Passage Times

Let X(t) be a temporally homogeneous irreducible Markov chain in continuous time defined on . For k < i < j, let H = {k + 1, ···, j − 1} and let kTij (jTik) be the upward (downward) conditional first-passage time of X(t) from i to j(k) given no visit to . These conditional passage times are studied through first-passage times of a modified chain HX(t) constructed by making the set of states absorbing. It will be shown that the densities of kTij and jTik for any birth-death process are unimodal and the modes kmij (jmik) of the unimodal densities are non-increasing (non-decreasing) with respect to i. Some distribution properties of kTij and jTik for a time-reversible Markov chain are presented. Symmetry among kTij, jTik, and is also discussed, where , and are conditional passage times of the reversed process of X(t).

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