## 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 17

Additional concepts we now introduce are those of

times for a given state. Suppose a state i is

Xn = i, we introduce a random variable Tt defined as follows: T i = m if Xn+k ^ i ...

Additional concepts we now introduce are those of

**recurrence**and first-passagetimes for a given state. Suppose a state i is

**recurrent**, and &{Xn = t} > 0. Given thatXn = i, we introduce a random variable Tt defined as follows: T i = m if Xn+k ^ i ...

Page 94

f«

0 Similarly, for processes we have the following. Definition: A process is called

f«

**recurrent**null according as its mean**recurrence**time t dHu(t) is finite or infinite.0 Similarly, for processes we have the following. Definition: A process is called

**recurrent**, ergodic,**recurrent**null, or transient if every one of its states has the ...Page 307

The arrival times form a

independent positive random variables. Let denote the mean and variance of T'{,

respectively. Let {t'i} denote the sequence of registration times. The sequence {t'{}

...

The arrival times form a

**recurrent**process; hence, the Tf are equidis- tributedindependent positive random variables. Let denote the mean and variance of T'{,

respectively. Let {t'i} denote the sequence of registration times. The sequence {t'{}

...

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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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