## 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. |

### From inside the book

Results 1-3 of 53

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 44

Albert T. Bharucha-Reid. In Chap. 3 the theory of diffusion processes will be

considered, and the representation of discrete

processes will be presented at that time. B. Random-walk and

Albert T. Bharucha-Reid. In Chap. 3 the theory of diffusion processes will be

considered, and the representation of discrete

**branching processes**as diffusionprocesses will be presented at that time. B. Random-walk and

**Branching****Processes**.Page 47

Hence Q = ^ forp^sg = 1 forp^g (1.118) The gambler's ruin problem represents

the following

< i < oo. Since the above random walk is equivalent to a twofold branching, the ...

Hence Q = ^ forp^sg = 1 forp^g (1.118) The gambler's ruin problem represents

the following

**branching process**: The population size in the zero generation is t, 0< i < oo. Since the above random walk is equivalent to a twofold branching, the ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

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 associated assume assumptions asymptotic birth process birth-and-death process branching processes cascade process cascade theory coefficient collision consider defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes distribution function electron-photon cascades epidemic exists expression Feller finite fluctuation problem functional equation given Hence initial condition integral equation interval ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random machine Markov chain Markov processes Math mathematical matrix mean and variance mean number Mellin transform Messel method Monte Carlo methods mutation neutron nonnegative nucleon nucleon cascades number of electrons number of individuals o(At obtain parameter photon Phys Poisson process probability distribution Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t reaction recurrent refer satisfies solution of Eq Statist stochastic model Stochastic Processes Theorem tion transition probabilities zero