## 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 113

It can be shown that F^^t) satisfies the differential equation ^=ft(FvFt) i = l,2 (2.230

) at with

fiM ^ + ftM ^ (2-232) at os1 o«2 From (2.230) and the definition of f{(sv8t) we ...

It can be shown that F^^t) satisfies the differential equation ^=ft(FvFt) i = l,2 (2.230

) at with

**initial condition***>i.«a.°) = *< (2.231) or the partial differential equation =fiM ^ + ftM ^ (2-232) at os1 o«2 From (2.230) and the definition of f{(sv8t) we ...

Page 138

where An,Bn, and Xn are determined by the

which must be specified for any particular diffusion problem. We now consider

the application of the Laplace transformation1 to the Kolmogorov diffusion

equations.

where An,Bn, and Xn are determined by the

**initial**and boundary**conditions**which must be specified for any particular diffusion problem. We now consider

the application of the Laplace transformation1 to the Kolmogorov diffusion

equations.

Page 389

which is to be solved with the

Eq. (9.34) that satisfies the above

<)} X ^1 — *£exP + [1 - y>(s)]A(r)}F (t,0) drj (9.35) where .F(t,0) is the probability ...

which is to be solved with the

**initial condition**95(0,5) = 1. The unique solution ofEq. (9.34) that satisfies the above

**initial condition**is <p(t,a) = exp {st — [1 - v(«)]A(<)} X ^1 — *£exP + [1 - y>(s)]A(r)}F (t,0) drj (9.35) where .F(t,0) is the probability ...

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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 |

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