## 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 34

Foster [20] has given a classifica- j = 1

the tru. A chain is termed dissipative if mu = 0 for all i and j; it is termed

semidissipative if tru = 0 for some i and j but X to < 1 for some i; and it is termed

co i = 1 ...

Foster [20] has given a classifica- j = 1

**tion**of chains based on the properties ofthe tru. A chain is termed dissipative if mu = 0 for all i and j; it is termed

semidissipative if tru = 0 for some i and j but X to < 1 for some i; and it is termed

co i = 1 ...

Page 154

Let F(s) = oo X p(x)s”, s| < 1, where p(x) is the probability that in the first generaa

= 0

Our purpose is to pass from the generating function associated with the simple ...

Let F(s) = oo X p(x)s”, s| < 1, where p(x) is the probability that in the first generaa

= 0

**tion**a individuals will beformed from a single individual present at time zero.Our purpose is to pass from the generating function associated with the simple ...

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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