## 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 64

Given a set of coefficients a,(t) satisfying (2.32) to (2.34), there exists a set of

functions P.,(r,t) = F,(r,t) that

, in general, be replaced by equality. Necessary and sufficient conditions are

given ...

Given a set of coefficients a,(t) satisfying (2.32) to (2.34), there exists a set of

functions P.,(r,t) = F,(r,t) that

**satisfy**(2.21) to (2.25). 2. The inequality (2.24) cannot, in general, be replaced by equality. Necessary and sufficient conditions are

given ...

Page 71

Albert T. Bharucha-Reid. The use of Theorem 2.2 enables us to obtain sufficient

conditions for uniqueness. We now consider the following: Theorem 2.3 (

Uniqueness Theorem): 1. If oo Fú(t) = 1 (2.77) i = 1 2 for some fixed i and if Pu(t)

Albert T. Bharucha-Reid. The use of Theorem 2.2 enables us to obtain sufficient

conditions for uniqueness. We now consider the following: Theorem 2.3 (

Uniqueness Theorem): 1. If oo Fú(t) = 1 (2.77) i = 1 2 for some fixed i and if Pu(t)

**satisfies**...Page 151

... the differential equation which yields $1(c) and $2(z) as solutions. The result

we need is given by the following theorem. Theorem 3.3: If f(zo;t,y) uniquely

(–oo; ...

... the differential equation which yields $1(c) and $2(z) as solutions. The result

we need is given by the following theorem. Theorem 3.3: If f(zo;t,y) uniquely

**satisfies**the backward Kolmogorov equation with boundary conditions f(oo;t,y) = f(–oo; ...

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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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