## 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 97

Similarly, if we differentiate (2.174) twice, we obtain the

= *| [m](t — t)]*q(t) dr + *s ma(t — t)q(t) dt (2.178) where K2 = X n(n − 1)ga. Since

mi(t) is a known function [obtained 2 n = by solving Eq. (2.177)], the first

Similarly, if we differentiate (2.174) twice, we obtain the

**integral**equation t t ma(t)= *| [m](t — t)]*q(t) dr + *s ma(t — t)q(t) dt (2.178) where K2 = X n(n − 1)ga. Since

mi(t) is a known function [obtained 2 n = by solving Eq. (2.177)], the first

**integral**...Page 273

Jánossy has shown that for 0 < e < 1 the factorial moments satisfy the

equation so-so "sis. (...)s.(...) 0 0 J0 m = 0 \70 e × So-n (:: y ..) w(e',e") de' de" dr +

6, e." (5.129) e with So(e,t) = 1. If we consider the

...

Jánossy has shown that for 0 < e < 1 the factorial moments satisfy the

**integral**equation so-so "sis. (...)s.(...) 0 0 J0 m = 0 \70 e × So-n (:: y ..) w(e',e") de' de" dr +

6, e." (5.129) e with So(e,t) = 1. If we consider the

**integral**equation for the mean,...

Page 444

e-*d F(t) (B.5) w—-oo o'0 0. exists for a certain value of A, say A*, we say that the

of convergence A, with the property that the

e-*d F(t) (B.5) w—-oo o'0 0. exists for a certain value of A, say A*, we say that the

**integral**(B.4) converges for A = A*. It can be shown that there exists an abscissaof convergence A, with the property that the

**integral**(B.5) converges if 3(A) > 2, ...### What people are saying - Write a review

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### Contents

Introduction | 1 |

Processes Discrete in Space and Continuous in Time | 57 |

Processes Continuous in Space and Time | 129 |

Copyright | |

9 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 addition applications approach arrival associated assume assumptions becomes birth boundary branching processes called cascade coefficients collision concerned condition consider constant continuous counter death defined denote density derive described determined developed differential equation diffusion discussion distribution function electron energy epidemic equal exists expected expression finite fluctuation given gives growth Hence independent individuals initial condition integral interest interval introduce Kolmogorov equations Laplace transform length limit machine Markov Markov chain Markov processes Math mathematical mean method moments necessary nucleon obtain particle particular photon Poisson population positive primary problem Proof properties queueing radiation random variable reaction refer relation represent respectively satisfies shown simple ſº solution Statist Stochastic Processes Theorem theory tion transition probabilities zero