## 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

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Page 125

dependent Branching Stochastic Processes in Cascade Theory, Phys. Rev., vol.

96, pp. 751-753, 1954. 12 Bharucha-Reid, A. T. : On the Stochastic Theory of

Epidemics ...

**Math**. Biophys., vol. 15, pp. 361-365, 1953. 11 Bharucha-Reid, A. T. : Age-dependent Branching Stochastic Processes in Cascade Theory, Phys. Rev., vol.

96, pp. 751-753, 1954. 12 Bharucha-Reid, A. T. : On the Stochastic Theory of

Epidemics ...

Page 126

32 Halmos, P. R.: "Measure Theory," D. Van Nostrand Company, Inc., Princeton,

N.J., 1950. 33 Harris, T. E.: Some

Proc. Second Berkeley Symposium on

32 Halmos, P. R.: "Measure Theory," D. Van Nostrand Company, Inc., Princeton,

N.J., 1950. 33 Harris, T. E.: Some

**Mathematical**Models for Branching Processes,Proc. Second Berkeley Symposium on

**Math**. Statistics and Probability, pp.Page 162

4 Darling, D. A., and A. J. F. Siegert: The First Passage Problem for a Continuous

Markov Process, Ann.

Theorie der stochastischen Prozesse (Existenz- und Eindeutigkeitssatze),

4 Darling, D. A., and A. J. F. Siegert: The First Passage Problem for a Continuous

Markov Process, Ann.

**Math**. Statist., vol. 24, pp. 624-639, 1953. 5 Feller, W. : ZurTheorie der stochastischen Prozesse (Existenz- und Eindeutigkeitssatze),

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### 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