## 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 49

As in the one-dimensional case, we can obtain the

differentiation of the generating function. In this case we define ml?' (1.123) as

the expected number of individuals of type j(j = 1, 2, . . . , N) in the nth generation

from one ...

As in the one-dimensional case, we can obtain the

**moments**of X„ bydifferentiation of the generating function. In this case we define ml?' (1.123) as

the expected number of individuals of type j(j = 1, 2, . . . , N) in the nth generation

from one ...

Page 97

While we have considered only the first two

shown that the fcth

provided the

While we have considered only the first two

**moments**, Bellman and Harris haveshown that the fcth

**moments**A(0 = t * = 1,2,... (2.179) 3=0 CO exist fort e [0,oo),provided the

**moments**2 nkqn exist for k = 1,2,.... n-0 The asymptotic theory ...Page 273

Hence, from (5.123) and (5.125), the ifcth factorial

= K*k Yk(sv ...,sk;P) (5.127) 2. ... We now consider the G-equations for a nucleon

cascade in homogeneous nuclear matter and obtain the

Hence, from (5.123) and (5.125), the ifcth factorial

**moment**is given by Tk(E0;E;t)= K*k Yk(sv ...,sk;P) (5.127) 2. ... We now consider the G-equations for a nucleon

cascade in homogeneous nuclear matter and obtain the

**moments**of the ...### 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