## 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 9

This theory will be developed with special reference to discrete

thought of as a representation of the generation-by-generation growth of a

population.

This theory will be developed with special reference to discrete

**branching****processes**. The mathematical model of a discrete**branching process**can bethought of as a representation of the generation-by-generation growth of a

population.

Page 10

the nonnegative integers and discuss the relationship between randomwalk

processes and

dimensional processes, i.e., processes in which the population is made up of N

different ...

the nonnegative integers and discuss the relationship between randomwalk

processes and

**branching processes**. Finally, in Sec. 1.8, we consider N-dimensional processes, i.e., processes in which the population is made up of N

different ...

Page 44

3 the theory of diffusion processes will be considered, and the representation of

discrete

time. B. Random-walk and

along ...

3 the theory of diffusion processes will be considered, and the representation of

discrete

**branching processes**as diffusion processes will be presented at thattime. B. Random-walk and

**Branching Processes**. A random walk is the motionalong ...

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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