## 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 12

B. Transition Probabilities and Markov

terminology of Markov chain theory, we call the conditional probability pif the

probability of a transition from the state i to the state j, and call P = (pit) the

of ...

B. Transition Probabilities and Markov

**Matrices**. In order to conform with theterminology of Markov chain theory, we call the conditional probability pif the

probability of a transition from the state i to the state j, and call P = (pit) the

**matrix**of ...

Page 14

The Markov

form of a partitioned

Markov

states.

The Markov

**matrix**associated with a decomposable chain can be written in theform of a partitioned

**matrix**; for example, Pi In the above, Pr and P2 representMarkov

**matrices**which describe the transitions within the two closed sets ofstates.

Page 63

Let us now consider the Kolmogorov equations in

2.31) g,( *)Q(i(t) = i#j and let A(t) = (a^t)). The elements atj(t) are continuous

functions of time with oĢ(0 >0 i^j (2.32) ati(t) < 0 (2.33) 00 and 2 a„(f ) < 0 for all t (

2.34) ...

Let us now consider the Kolmogorov equations in

**matrix**form. Put q{(t) = —a{i(t) (2.31) g,( *)Q(i(t) = i#j and let A(t) = (a^t)). The elements atj(t) are continuous

functions of time with oĢ(0 >0 i^j (2.32) ati(t) < 0 (2.33) 00 and 2 a„(f ) < 0 for all t (

2.34) ...

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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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