## 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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Results 1-3 of 85

Page 107

If r is not a limit point of the process [i.e., the process satisfying that initial

condition os()) = n], then from Theorem 2.12 we

From the Kolmogorov equations dP., (t dPost) = a, P.,(t) + Xa, PA(t) dt k # 3 we

If r is not a limit point of the process [i.e., the process satisfying that initial

condition os()) = n], then from Theorem 2.12 we

**obtain**s P.(t) dr & Co (2.215) 0From the Kolmogorov equations dP., (t dPost) = a, P.,(t) + Xa, PA(t) dt k # 3 we

**obtain**the ...Page 151

If we now introduce (3.89) for g;(s;z) and go.(s.20) in the above system, we

(3.90) and (3.91). Finally, (3.92) is

ri, r2) = h (8,20;ri,fa) + h;(s,aro; fire), since from (3.87) G(t,xo,r1,r2) = Hi(t,xo;ri,fa) ...

If we now introduce (3.89) for g;(s;z) and go.(s.20) in the above system, we

**obtain**(3.90) and (3.91). Finally, (3.92) is

**obtained**from the above by noting that g”(8,20;ri, r2) = h (8,20;ri,fa) + h;(s,aro; fire), since from (3.87) G(t,xo,r1,r2) = Hi(t,xo;ri,fa) ...

Page 177

If we assume that at time t = 0 the population is made up of only one female, then

the initial conditions to be imposed are P.,(0) = 1 for a = 1 = 0 for a # 1 (4.42) We

do not attempt to solve the above system in order to

If we assume that at time t = 0 the population is made up of only one female, then

the initial conditions to be imposed are P.,(0) = 1 for a = 1 = 0 for a # 1 (4.42) We

do not attempt to solve the above system in order to

**obtain**explicit expressions ...### 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

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