## 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 38

In order to establish the

classical result due to Konigs [48] i1 If the function 6(8) is analytic in a given

domain D with 6(80) = 80 and |0'(«o)| = a < 1 for some «0 e D, then in this domain

[6n(8) ...

In order to establish the

**functional equation**satisfied by G(8), we utilize aclassical result due to Konigs [48] i1 If the function 6(8) is analytic in a given

domain D with 6(80) = 80 and |0'(«o)| = a < 1 for some «0 e D, then in this domain

[6n(8) ...

Page 98

In this case, the probability that n = 0 X(t) = 0, for some time t, is given by the

unique nonnegative root, less than unity, of the

2.181) where h(s) is defined by (2.175). D. Some Branching Models Based on

Specific ...

In this case, the probability that n = 0 X(t) = 0, for some time t, is given by the

unique nonnegative root, less than unity, of the

**functional equation**h(s) = s (2.181) where h(s) is defined by (2.175). D. Some Branching Models Based on

Specific ...

Page 391

(9.41) nl If n = 0, only one customer is served, and the associated distribution

function is H(x). If n > 1, the server, after serving ... y>[a + A - XT(s)] (9.44) This

function ...

(9.41) nl If n = 0, only one customer is served, and the associated distribution

function is H(x). If n > 1, the server, after serving ... y>[a + A - XT(s)] (9.44) This

**functional equation**for T(s) was first obtained by Kendall [37]. The distributionfunction ...

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

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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