## 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 65

construction of an infinite matrix F(t) = (Fu(t)) which

equations. = F(t)A (2.43) dt = AF(t) (2.44) dt with F(0) = /. The method of

construction1 utilizes the nth section of A, that is, an n X n matrix A{n), to find a

solution F<n)(t) ...

construction of an infinite matrix F(t) = (Fu(t)) which

**satisfies**the Kolmogorovequations. = F(t)A (2.43) dt = AF(t) (2.44) dt with F(0) = /. The method of

construction1 utilizes the nth section of A, that is, an n X n matrix A{n), to find a

solution F<n)(t) ...

Page 71

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 2*7,(0

= 1 (2.77) ,=i for some fixed i and if PiS(t)

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 2*7,(0

= 1 (2.77) ,=i for some fixed i and if PiS(t)

**satisfies**(2.69), Pit(t) ^ 0 and I Pi,(t) < 1 ...Page 151

... functions ^(x) and f2(a;), we now consider the differential equation which yields

fx(x) and f2(a;) 8,8 solutions. The result we need is given by the following

theorem. Theorem 3.3: If f(x0;t,y) uniquely

equation ...

... functions ^(x) and f2(a;), we now consider the differential equation which yields

fx(x) and f2(a;) 8,8 solutions. The result we need is given by the following

theorem. Theorem 3.3: If f(x0;t,y) uniquely

**satisfies**the backward Kolmogorovequation ...

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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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