## 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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Results 1-3 of 46

Page 168

4.2

systems is that of

populations, bacterial or human populations, a useful theory of

is ...

4.2

**Growth**of Populations A. Introduction. A property common to biologicalsystems is that of

**growth**. Hence, whether we are concerned with animal or plantpopulations, bacterial or human populations, a useful theory of

**growth**processesis ...

Page 169

In this section, which has six subsections, we consider some of the stochastic

models of population

Markov processes. These subsections are concerned with birth-and-death type ...

In this section, which has six subsections, we consider some of the stochastic

models of population

**growth**that have been developed by using the theory ofMarkov processes. These subsections are concerned with birth-and-death type ...

Page 192

4.3

considered the

homogeneous populations) or two or more types of organism (heterogeneous ...

4.3

**Growth**of Populations Subject to Mutation A. Introduction. In Sec. 4.2 weconsidered the

**growth**of populations consisting of either one type of organism (homogeneous populations) or two or more types of organism (heterogeneous ...

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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