## 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 57

Page 103

The chain denned by the above transition probabilities is aperiodic, since Pu(tit)

> 0, and, therefore, lim Pit(nT)

continuity1 of the transition probabilities for i and j fixed, it follows that this limit is

...

The chain denned by the above transition probabilities is aperiodic, since Pu(tit)

> 0, and, therefore, lim Pit(nT)

**exists**for each fixed t > 0. Now, from the uni- formcontinuity1 of the transition probabilities for i and j fixed, it follows that this limit is

...

Page 310

In this case we say that a stationary distribution of X(t)

Finally, we consider the case when t is a random variable uniformly distributed

over the interval (0,T). Let QT{x,t) = 0>{X(t + t) - X(r) < x} From (6.61) we have QT(x

,t) ...

In this case we say that a stationary distribution of X(t)

**exists**in the weak sense.Finally, we consider the case when t is a random variable uniformly distributed

over the interval (0,T). Let QT{x,t) = 0>{X(t + t) - X(r) < x} From (6.61) we have QT(x

,t) ...

Page 395

distribution of waiting times

lim Fn(t) = F(t)

Theorem 9.10: A necessary and sufficient condition that lim F„(t) = F(t)

that ...

distribution of waiting times

**exists**; i.e., when does the limiting distribution functionlim Fn(t) = F(t)

**exist**? This question is answered by the following theorem.Theorem 9.10: A necessary and sufficient condition that lim F„(t) = F(t)

**exists**isthat ...

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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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