## 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

that X n = i, we introduce a random variable Tt denned as follows: Tt = m if Xn+k ^

t ...

Additional concepts we now introduce are those of

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

**recurrent**, and &{Xn — i) > 0. Giventhat X n = i, we introduce a random variable Tt denned as follows: Tt = m if Xn+k ^

t ...

Page 93

We can now define the states as follows: Definition : The tth state is

1 and transient if / # 1. If » is a

A continuant is a matrix with nonzero elements on the lower diagonal, diagonal, ...

We can now define the states as follows: Definition : The tth state is

**recurrent**if / =1 and transient if / # 1. If » is a

**recurrent**state, it can be classified asergrodic or 1A continuant is a matrix with nonzero elements on the lower diagonal, diagonal, ...

Page 94

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

**recurrent**null according as its mean**recurrence**time I t dHH(t) is finite or infinite.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 ...### What people are saying - Write a review

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### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

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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