## 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 227

In the case of low

n can be interpreted as the number of hits with photons (or

is therefore independent of the

In the case of low

**radiation**intensities this knowledge is not easy to obtain. Sincen can be interpreted as the number of hits with photons (or

**radiation**quanta) andis therefore independent of the

**radiation**intensity, a sufficient degree of ...Page 240

This number is 2 dE dtj"y(W,t)n(^^ = 2 dE */V(j <) * (3-D In (5.1) y>0(u), which is

the differential probability for pair production per

complete screening, is given by tp0(u) = [u* + (1 - «)2] + [(I - 26)«(1 - u)] where u ...

This number is 2 dE dtj"y(W,t)n(^^ = 2 dE */V(j <) * (3-D In (5.1) y>0(u), which is

the differential probability for pair production per

**radiation**length in the case ofcomplete screening, is given by tp0(u) = [u* + (1 - «)2] + [(I - 26)«(1 - u)] where u ...

Page 351

The mathematical problems in radiative transfer theory are, in the main,

concerned with the solution of an integrodifFerential equation for the specific

intensity of

the nature of ...

The mathematical problems in radiative transfer theory are, in the main,

concerned with the solution of an integrodifFerential equation for the specific

intensity of

**radiation**. The particular equation involved will depend, of course, onthe nature of ...

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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