## 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 39

Albert T. Bharucha-Reid. It is clear from the above that the limiting distribution p”(

z) will depend on the particular generating function F(s) and will assume a

number of forms depending on the

by ...

Albert T. Bharucha-Reid. It is clear from the above that the limiting distribution p”(

z) will depend on the particular generating function F(s) and will assume a

number of forms depending on the

**expected**value m. A special case was studiedby ...

Page 183

Aimu(t) - ulimia(t) – unaffiu(t) dmai() Azmai(t) – usiñ11(t) – usemes(t) dt It is of

interest to compare this system of equations for the

with the deterministic system ...

Aimu(t) - ulimia(t) – unaffiu(t) dmai() Azmai(t) – usiñ11(t) – usemes(t) dt It is of

interest to compare this system of equations for the

**expected**population sizeswith the deterministic system ...

Page 197

... t)e” dr (4.98) 0 From (4.97) and (4.98) the

population is easily determined. We have m(t) = &{Y(t)} = *so — r)e” dr (4.99) 0

where m(t) is the

... t)e” dr (4.98) 0 From (4.97) and (4.98) the

**expected**number of mutants in thepopulation is easily determined. We have m(t) = &{Y(t)} = *so — r)e” dr (4.99) 0

where m(t) is the

**expected**number of descendants of a BIOLOGY 197.### 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