## Elements of the theory of Markov processes and their applicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |

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Results 1-3 of 31

Page 13

1.6 we shall study the

study the

States. Given a Markov chain {Xn, n — 0, 1, . . .}, its states can be classified in a ...

1.6 we shall study the

**asymptotic**behavior of the p^p, which in turn enables us tostudy the

**asymptotic**behavior of the absolute probabilities. D. Classification ofStates. Given a Markov chain {Xn, n — 0, 1, . . .}, its states can be classified in a ...

Page 97

(2.179) 3=0 CO exist fort e [0,oo), provided the moments 2 nkqn exist for k = 1,2,...

. n-0 The

Harris to discuss the limiting behavior of the moments fik. In particular, it has ...

(2.179) 3=0 CO exist fort e [0,oo), provided the moments 2 nkqn exist for k = 1,2,...

. n-0 The

**asymptotic**theory developed by Feller has been uBed by Bellman andHarris to discuss the limiting behavior of the moments fik. In particular, it has ...

Page 263

The above results give the

tending to infinity. Hence, (5.87) is the first approximation for the distribution

function for very large depth of absorber. The above results also admit an

interpretation ...

The above results give the

**asymptotic**solution of the distribution function for ttending to infinity. Hence, (5.87) is the first approximation for the distribution

function for very large depth of absorber. The above results also admit an

interpretation ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

Copyright | |

10 other sections not shown

### Other editions - View all

Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |

Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |

### Common terms and phrases

absorber Acad applications associated assume assumptions asymptotic birth process birth-and-death process branching processes cascade process cascade theory coefficient collision consider defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes distribution function electron-photon cascades epidemic exists expression Feller finite fluctuation problem functional equation given Hence initial condition integral equation interval ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random machine Markov chain Markov processes Math mathematical matrix mean and variance mean number Mellin transform Messel method Monte Carlo methods mutation neutron nonnegative nucleon nucleon cascades number of electrons number of individuals o(At obtain parameter photon Phys Poisson process probability distribution Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t reaction recurrent refer satisfies solution of Eq Statist stochastic model Stochastic Processes Theorem tion transition probabilities zero