## 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 95

This process,

Bellman-Harris process is of considerable importance in many fields of

application, since, as we shall see, it incorporates several features which enable

the ...

This process,

**described**by Bellman and Harris [9], is called agedependent." TheBellman-Harris process is of considerable importance in many fields of

application, since, as we shall see, it incorporates several features which enable

the ...

Page 99

(2.187) Solving this equation with initial condition F(s,0) = 8 yields (2.150). 4. A

Non-Markovian Birth Process. Kendall [50,51] has considered a non-Markovian

binary birth process which can be

(2.187) Solving this equation with initial condition F(s,0) = 8 yields (2.150). 4. A

Non-Markovian Birth Process. Kendall [50,51] has considered a non-Markovian

binary birth process which can be

**described**as a multiple-phase birth process.Page 239

In case we consider energies which are large compared with the critical energy,

we have: APPROxIMATION A: 1. Radiation phenomena (Bremsstrahlung) and

pair production can be

energies ...

In case we consider energies which are large compared with the critical energy,

we have: APPROxIMATION A: 1. Radiation phenomena (Bremsstrahlung) and

pair production can be

**described**by the asymptotic formulas for very highenergies ...

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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