## 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 11

is such that the conditional probability distribution of X, 11 depends only on the

value of X, and is independent of all previous values, we say that the process has

the Markov property and call it a

is such that the conditional probability distribution of X, 11 depends only on the

value of X, and is independent of all previous values, we say that the process has

the Markov property and call it a

**Markov chain**. More precisely, *{X,+1 = 2,11|Xn ...Page 13

This functional equation, which characterizes

importance in the theory of

establishes the connection between

of ...

This functional equation, which characterizes

**Markov chains**, is of fundamentalimportance in the theory of

**Markov chains**, and it is this equation whichestablishes the connection between

**Markov chains**and the theory of semigroupsof ...

Page 377

We first consider the

representation being based on the concept of an imbedded

we consider the representation of queueing systems as Markov processes.

We first consider the

**Markov chain**representation of queueing systems, thisrepresentation being based on the concept of an imbedded

**Markov chain**. Nextwe consider the representation of queueing systems as Markov processes.

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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