## 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 29

Tipt; [1.60] =0 with X tr, a 1, and the distribution {T,} is uniquely determined. j=0

Proof: By hypothesis, the states j have

MF". Now p? —- try; hence, (1.61) holds for i = j. For any fixed i we have X K?

Tipt; [1.60] =0 with X tr, a 1, and the distribution {T,} is uniquely determined. j=0

Proof: By hypothesis, the states j have

**finite**mean recurrence times M. Let m, =MF". Now p? —- try; hence, (1.61) holds for i = j. For any fixed i we have X K?

Page 267

B. Equations for Nucleon Cascades in Homogeneous Nuclear Matter and in a

nucleon cascades in homogeneous nuclear matter and in a

nucleon ...

B. Equations for Nucleon Cascades in Homogeneous Nuclear Matter and in a

**Finite**Absorber. In this section we consider the fundamental equations fornucleon cascades in homogeneous nuclear matter and in a

**finite**absorber. Anucleon ...

Page 399

infinite and

only m calls are being handled, and we have in this case Auz = mu, for a > m.

Hence, for a 3 m the Kolmogorov equations in the

by ...

infinite and

**finite**channel cases. However, if the system is in state z with a > m,only m calls are being handled, and we have in this case Auz = mu, for a > m.

Hence, for a 3 m the Kolmogorov equations in the

**finite**channel case are givenby ...

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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