## 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 187

2.5 the Bellman-Harris process, termed age-dependent, was introduced and

certain of its

s,t) for the probabilities P.(t) satisfies the Stieltjes integral equation F(s,t) –sor. t – t

)] ...

2.5 the Bellman-Harris process, termed age-dependent, was introduced and

certain of its

**properties**were studied. It was shown that the generating function F(s,t) for the probabilities P.(t) satisfies the Stieltjes integral equation F(s,t) –sor. t – t

)] ...

Page 283

It has been suggested that this function has more elegant mathematical

suitable for the study of cascade processes in nuclear emulsions and in the

bubble chamber.

It has been suggested that this function has more elegant mathematical

**properties**than the distribution function usually studied and that it is moresuitable for the study of cascade processes in nuclear emulsions and in the

bubble chamber.

Page 377

necessary to consider various ways of representing queueing systems so that

their stochastic

problems arising in the theory of telephone traffic, and in Sec. 9.4 we consider ...

necessary to consider various ways of representing queueing systems so that

their stochastic

**properties**can be ascertained. In Sec. 9.3 we consider queueingproblems arising in the theory of telephone traffic, and in Sec. 9.4 we consider ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Continuous in Time | 57 |

Processes Continuous in Space and Time | 129 |

Copyright | |

9 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 addition applications approach arrival associated assume assumptions becomes birth boundary branching processes called cascade coefficients collision concerned condition consider constant continuous counter death defined denote density derive described determined developed differential equation diffusion discussion distribution function electron energy epidemic equal exists expected expression finite fluctuation given gives growth Hence independent individuals initial condition integral interest interval introduce Kolmogorov equations Laplace transform length limit machine Markov Markov chain Markov processes Math mathematical mean method moments necessary nucleon obtain particle particular photon Poisson population positive primary problem Proof properties queueing radiation random variable reaction refer relation represent respectively satisfies shown simple ſº solution Statist Stochastic Processes Theorem theory tion transition probabilities zero