## 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 180

In this section we formulate a general stochastic model of interaction between

two species and then

interest. Before

In this section we formulate a general stochastic model of interaction between

two species and then

**consider**several special cases of this model that are ofinterest. Before

**considering**the stochastic model, we give a brief sketch of two ...Page 238

In this chapter we

cascade process within the framework of the theory of stochastic processes. That

is, we

...

In this chapter we

**consider**the problem of formulating the development of acascade process within the framework of the theory of stochastic processes. That

is, we

**consider**the problem of determining the probability distribution of the state...

Page 377

necessary to

their stochastic properties can be ascertained. In Sec. 9.3 we

problems arising in the theory of telephone traffic, and in Sec. 9.4 we

necessary to

**consider**various ways of representing queueing systems so thattheir stochastic properties can be ascertained. In Sec. 9.3 we

**consider**queueingproblems arising in the theory of telephone traffic, and in Sec. 9.4 we

**consider**...### What people are saying - Write a review

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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