## 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)

The problem is to determine the

**probability**that x individuals will migrate from JB!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)

**denote**the number of individuals in region ...Page 259

In this case let <l)(0(e,n;<)

particles in the cascade. The superscript » = 1 if the primary particle is an electron

, and i = 2 if the primary particle is a photon. In the definition of <S>li)(e,n;t) we ...

In this case let <l)(0(e,n;<)

**denote the probability**that at thickness t there are nparticles in the cascade. The superscript » = 1 if the primary particle is an electron

, and i = 2 if the primary particle is a photon. In the definition of <S>li)(e,n;t) we ...

Page 349

Since the observer is at the origin of the coordinate system, and since we are in

Euclidean 3-space, the distance f is simply f = («• + y2 + z2)* We

the

Since the observer is at the origin of the coordinate system, and since we are in

Euclidean 3-space, the distance f is simply f = («• + y2 + z2)* We

**denote**by 0(f)the

**probability**that the photograph will contain a noticeable image of the galaxy.### What people are saying - Write a review

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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