## 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 14

Page 292

58 Messel, H.: Further Results on the

Cascade Theory and the Probability Distribution Function, Proc. Phya. Soc. (

London), ser. A, vol. 64, pp. 807-813, 1951. 59 Messel, H.: The Solution of the ...

58 Messel, H.: Further Results on the

**Fluctuation Problem**in Electron- PhotonCascade Theory and the Probability Distribution Function, Proc. Phya. Soc. (

London), ser. A, vol. 64, pp. 807-813, 1951. 59 Messel, H.: The Solution of the ...

Page 346

w (7.44) *"°IT(ai — «*) i = 0 where an = n(l — na2r) We close this discussion of a

stochastic model of a

some ...

w (7.44) *"°IT(ai — «*) i = 0 where an = n(l — na2r) We close this discussion of a

stochastic model of a

**fluctuating**density field ... We close this section on the**problem**of**fluctuations**in brightness of the Milky Way with brief comments onsome ...

Page 465

... 81, 92 Dissipative chain, 34 Ehrenfest process, 122 Electron-photon cascade,

235

probability distribution of, 353, 354 Epidemic curve. 203 Epidemics, small groups,

...

... 81, 92 Dissipative chain, 34 Ehrenfest process, 122 Electron-photon cascade,

235

**fluctuation problem**for, 246-265 Elementary return process, 145 Emission,probability distribution of, 353, 354 Epidemic curve. 203 Epidemics, small groups,

...

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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