## 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

K% \\mi{t - T)?q(r) dr + Kt \m2(t - t)?(t) dr (2.178) Jo Jo CO where K2 = "£n(n — l)

qn. Since mx(<) is a known function [obtained a-g by solving Eq. (2.177)], the first

...

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

**integral equation**m2(t) =K% \\mi{t - T)?q(r) dr + Kt \m2(t - t)?(t) dr (2.178) Jo Jo CO where K2 = "£n(n — l)

qn. Since mx(<) is a known function [obtained a-g by solving Eq. (2.177)], the first

...

Page 101

Hence, the equation for the generating function becomes Jo n=0 I qn(T)F"(8, t - r)

g(r) dr =o = I '{1 - 0e— ' + ... Differentiation of (2.195) gives the

^f) = X(fi + y) »»4(t - T)e-(,+A,r dr + e~xt Jo which can, in turn, be reduced to the ...

Hence, the equation for the generating function becomes Jo n=0 I qn(T)F"(8, t - r)

g(r) dr =o = I '{1 - 0e— ' + ... Differentiation of (2.195) gives the

**integral equation**m^f) = X(fi + y) »»4(t - T)e-(,+A,r dr + e~xt Jo which can, in turn, be reduced to the ...

Page 273

5.2C the Janossy G-equations were derived for both nucleon and electron-

photon cascades. We now consider the ... It has been shown that G(e,z;t) satisfies

the

5.2C the Janossy G-equations were derived for both nucleon and electron-

photon cascades. We now consider the ... It has been shown that G(e,z;t) satisfies

the

**integral equation**G{e*;t) =j^e~"U~')\XjC°G{L;z'' T)°i^ ' z' T)w^''€") de' de" dr ...### 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

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