## 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 190

Hence, in order to characterize a particular growth process, it is necessary to

specify the

equation representation of two population growth processes. The processes we ...

Hence, in order to characterize a particular growth process, it is necessary to

specify the

**coefficients**asa:) and b(ac). In this section we consider the diffusion-equation representation of two population growth processes. The processes we ...

Page 214

In order to characterize the diffusion process associated with a given genetic

situation, it is necessary to specify the

other quantities, which occur in the forward system (4.137). As pointed out in

Chap.

In order to characterize the diffusion process associated with a given genetic

situation, it is necessary to specify the

**coefficients**asa:) and b(ac), as well as theother quantities, which occur in the forward system (4.137). As pointed out in

Chap.

Page 413

and the

(m, r, pus?) r – b The operative efficiency is defined as the ratio of the number of

machines waiting to be serviced to the number of repairmen; hence, b S(m = 1, r,

...

and the

**coefficient**of loss for repairmen, which is 1 — S(m – 1, r, pus?) (9.129) r S(m, r, pus?) r – b The operative efficiency is defined as the ratio of the number of

machines waiting to be serviced to the number of repairmen; hence, b S(m = 1, r,

...

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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