## 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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Results 1-3 of 14

Page 238

between the nucleon cascade and the electron -photon cascade, even though

the multiplicative processes involved in the ... The first problem we consider is

that of determining the mean

given ...

between the nucleon cascade and the electron -photon cascade, even though

the multiplicative processes involved in the ... The first problem we consider is

that of determining the mean

**number of electrons**and photons produced in agiven ...

Page 262

Urbanik, has shown that for large depth of the absorber the mean number of

particles 8{j(t,t) is of the same order of ... have also investigated the asymptotic

behavior of the ratio of the mean number of photons to the mean

Urbanik, has shown that for large depth of the absorber the mean number of

particles 8{j(t,t) is of the same order of ... have also investigated the asymptotic

behavior of the ratio of the mean number of photons to the mean

**number of****electrons**.Page 264

It is clear that in the case of electron-photon cascades the characteristic

functional will have two arbitrary argument functions, say ft(E) and t](E),

associated with the random variables representing the

photons, ...

It is clear that in the case of electron-photon cascades the characteristic

functional will have two arbitrary argument functions, say ft(E) and t](E),

associated with the random variables representing the

**number of electrons**andphotons, ...

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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