## 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 42

In addition to the

Z defined as Z =X X, (1.100) n = 0 That is, Z is the cumulative population size, or

the total number of individuals in all generations. We have already shown (Sec.

In addition to the

**random variable**Xa, it is of interest to study the**random variable**Z defined as Z =X X, (1.100) n = 0 That is, Z is the cumulative population size, or

the total number of individuals in all generations. We have already shown (Sec.

Page 264

In particular, it can be used to study the joint distribution of a continuous infinity of

powerful tool for studying the structure of stochastic processes, was introduced in

...

In particular, it can be used to study the joint distribution of a continuous infinity of

**random variables**. The characteristic functional, which appears to be a verypowerful tool for studying the structure of stochastic processes, was introduced in

...

Page 441

We remark that the above theorem can easily be extended to the case of N

independent

function of the sum of N independent

the ...

We remark that the above theorem can easily be extended to the case of N

independent

**random variables**. In this case we obtain the result: The generatingfunction of the sum of N independent

**random variables**is the N-fold product ofthe ...

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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