## 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 222

D. Some Additional

theory presented in Chap. 3. 1. First-passage Time

Classes.

D. Some Additional

**Problems**. In this section we discuss briefly several additional**problems**in the theory of gene frequencies that can be treated by using thetheory presented in Chap. 3. 1. First-passage Time

**Problems**for the FiredClasses.

Page 288

A more realistic treatment of this

Mathews [85]. These authors obtain an expression for the probability of

absorption and the probability density function of the range under the

assumptions that the ...

A more realistic treatment of this

**problem**has been given by Ramakrishnan andMathews [85]. These authors obtain an expression for the probability of

absorption and the probability density function of the range under the

assumptions that the ...

Page 292

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Messel, H.:

Further Results on the Fluctuation

and the Probability Distribution Function, Proc. Phys. Soc. (London), ser. A, vol.

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Messel, H.:

Further Results on the Fluctuation

**Problem**in ElectronPhoton Cascade Theoryand the Probability Distribution Function, Proc. Phys. Soc. (London), ser. A, vol.

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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