## 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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Page 45

C.

consider the relationship between the classical

problem of extinction of a population after n generations. The

problem is ...

C.

**Gambler's Ruin**and the Problem of Extinction of a Population. We nowconsider the relationship between the classical

**gambler's ruin**problem and theproblem of extinction of a population after n generations. The

**gambler's ruin**problem is ...

Page 46

1 1 3) is the generating function of the probability of absorption of x = 0 (ruin) at

the nth trial. ... type branching process and the

necessary to consider the case when a = oo, that is, the case in which x == 0 is

the only ...

1 1 3) is the generating function of the probability of absorption of x = 0 (ruin) at

the nth trial. ... type branching process and the

**gambler's ruin**problem, it isnecessary to consider the case when a = oo, that is, the case in which x == 0 is

the only ...

Page 465

98, 170, 171, 179, 191 (See also Fundamental theorem for branching processes ;

Lundberg theorem, 81, 82, 91 Final class, 50 First-passage time, 17, 93, 148 ...

98, 170, 171, 179, 191 (See also Fundamental theorem for branching processes ;

**Gambler's ruin**problem) Feller integrodifferential equations, 60, 120 Feller-Lundberg theorem, 81, 82, 91 Final class, 50 First-passage time, 17, 93, 148 ...

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

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 assume assumptions asymptotic birth process birth-and-death process cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function electron-photon cascades epidemic exists expression extinction Feller finite fluctuation functional equation gambler's ruin given Hence independent initial condition integral equation interval introduce ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random limit theorems machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon nucleon cascades number of individuals o(At obtain photon Poisson process population positive probability distribution problem Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t random walk recurrent refer satisfies sequence Statist stochastic model Stochastic Processes tion transition probabilities zero