## 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

Hence (1.17) must converge. Additional concepts we now introduce are those of

defined ...

Hence (1.17) must converge. Additional concepts we now introduce are those of

**recurrence**and first-passage times for a given state. Suppose a state i is**recurrent**, and 3°(X, <= i) > 0. Given that X, − i, we introduce a random variable T,defined ...

Page 93

Let Hu(t) = %X(t) = j for some t e (0,t] | X(0) = } i # j and Ha(t) = %X(T1) # i, X(ta) = i

for some T1, T2, 0 < r < r < t |X(0) = i\ Hence, H.,(t) and Hi(t) are the first-passage

time and

Let Hu(t) = %X(t) = j for some t e (0,t] | X(0) = } i # j and Ha(t) = %X(T1) # i, X(ta) = i

for some T1, T2, 0 < r < r < t |X(0) = i\ Hence, H.,(t) and Hi(t) are the first-passage

time and

**recurrence**time distributions, respectively. The integral I -sah,0 0 is the ...Page 94

oo

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

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**recurrent**null according as its mean**recurrence**time s t dh,(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 ...### What people are saying - Write a review

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### Contents

Introduction | 1 |

Processes Discrete in Space and Continuous in Time | 57 |

Processes Continuous in Space and Time | 129 |

Copyright | |

9 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 |

### Common terms and phrases

absorber addition applications approach arrival associated assume assumptions becomes birth boundary branching processes called cascade coefficients collision concerned condition consider constant continuous counter death defined denote density derive described determined developed differential equation diffusion discussion distribution function electron energy epidemic equal exists expected expression finite fluctuation given gives growth Hence independent individuals initial condition integral interest interval introduce Kolmogorov equations Laplace transform length limit machine Markov Markov chain Markov processes Math mathematical mean method moments necessary nucleon obtain particle particular photon Poisson population positive primary problem Proof properties queueing radiation random variable reaction refer relation represent respectively satisfies shown simple ſº solution Statist Stochastic Processes Theorem theory tion transition probabilities zero