## 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 46

Page 73

each case we

probability law of the process and obtain the solution of the equation and discuss

its properties. For the birth and birth-and-death processes the problems of

uniqueness ...

each case we

**derive**the differential-difference equation describing theprobability law of the process and obtain the solution of the equation and discuss

its properties. For the birth and birth-and-death processes the problems of

uniqueness ...

Page 256

In 1 950, Jdnossy1 [40] utilized the method of regeneration points to

diffusion equations satisfied by the generating function of the probability

distribution associated with a cascade process. The diffusion equations obtained

by ...

In 1 950, Jdnossy1 [40] utilized the method of regeneration points to

**derive**thediffusion equations satisfied by the generating function of the probability

distribution associated with a cascade process. The diffusion equations obtained

by ...

Page 257

The G-equations were first

an electron-photon cascade was considered. Hence, we will first

equations for the nucleon cascade and then consider the G-equations for the ...

The G-equations were first

**derived**for a nucleon cascade, and then the form foran electron-photon cascade was considered. Hence, we will first

**derive**the G-equations for the nucleon cascade and then consider the G-equations for the ...

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

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 assume assumptions asymptotic birth process birth-and-death process cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function electron-photon cascades epidemic exists expression extinction Feller finite fluctuation functional equation gambler's ruin given Hence independent initial condition integral equation interval introduce ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random limit theorems machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon nucleon cascades number of individuals o(At obtain photon Poisson process population positive probability distribution problem Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t random walk recurrent refer satisfies sequence Statist stochastic model Stochastic Processes tion transition probabilities zero