## 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 185

The problem is to determine the

to R2 in the time interval [0,t). The models considered in this section are due to

Pyke.1 Let the random variable X(t)

R2 ...

The problem is to determine the

**probability**that x individuals will migrate from Rxto R2 in the time interval [0,t). The models considered in this section are due to

Pyke.1 Let the random variable X(t)

**denote**the number of individuals in regionR2 ...

Page 228

The forward transition probabilities (4.189) represent transmission, and the

reverse transition probabilities (4.190) represent recovery. Conditions ... Let Q0

and Qn

respectively.

The forward transition probabilities (4.189) represent transmission, and the

reverse transition probabilities (4.190) represent recovery. Conditions ... Let Q0

and Qn

**denote the probabilities**of recovery and observable damage,respectively.

Page 259

Let ^'"(e) de dt

energy E omits a photon of energy eE in the (Ee, Ee -\- E de) and let w(2,(e) de dt

Let ^'"(e) de dt

**denote the probability**that in the interval (t, t + dt) an electron ofenergy E omits a photon of energy eE in the (Ee, Ee -\- E de) and let w(2,(e) de dt

**denote the probability**that in the interval (t, t + CASCADE THEORY 259.### 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