## Elements of the Theory of Markov Processes and Their ApplicationsThe purpose of this excellent graduate-level text is twofold: first, to present a nonmeasure-theoretic introduction to Markov processes, and second, to give a formal treatment of mathematical models based on this theory, which have been employed in various fields. Since the main emphasis is on application, the book is intended both as a text and reference in applied probability theory. There are three parts: Part I consists of three chapters, respectively devoted to processes discrete in space and time, processes discrete in space and continuous in time, and processes continuous in space and time (diffusion processes). Inasmuch as this section presents the elements of the theory necessary for the applications in Part II, this material can also serve as a text for an introductory course on Markov processes for students of probability and mathematical statistics, and research worked in applied fields. Part II consists of six chapters devoted to applications in biology, physics, astronomy and astrophysics, chemistry, and operations research. An attempt has been made to consider in detail representative applications of the theory of Markov processes in the above areas, with particular emphasis on the assumptions on which the stochastic models are based and the properties of these models. The three appendixes are concerned with generating functions, integral transforms, and Monte Carlo methods. The first two appendixes list some properties of generating functions and Laplace and Mellin transforms required in the text. The third appendix is mainly devoted to references dealing with the use of Monte Carlo methods in the study of stochastic processes occurring in different applied fields. A bibliography is given at the end of each chapter and appendix. In addition, a general bibliography of texts and monographs on stochastic processes is given at the end of the Introduction. Prerequisites are a knowledge of elementary probability theory, mathematical statistics and analysis. |

### From inside the book

Results 1-3 of 48

Page 43

individuals are identical and statistically independent, then the probability of

producing a total of n individuals in the succeeding k generations is the

individuals in ...

individuals are identical and statistically independent, then the probability of

producing a total of n individuals in the succeeding k generations is the

**coefficient**of s” in [Goss)]'. Thus q.m - X %X1 = }3^{of producing a total of n – iindividuals in ...

Page 196

Y(t)} – !---wo — 1) F *[G, + yo)e(*** - !/1] se-to-ti) - east-o] (4.90) 0. From (4.89) we

observe that the regression of Y(t2) on Y(ti) is linear; hence, &{Y(t.)[Y(ti) — & {Y(t)}

]} = b, 12*{Y(t)} (4.91) where ball is the regression

Y(t)} – !---wo — 1) F *[G, + yo)e(*** - !/1] se-to-ti) - east-o] (4.90) 0. From (4.89) we

observe that the regression of Y(t2) on Y(ti) is linear; hence, &{Y(t.)[Y(ti) — & {Y(t)}

]} = b, 12*{Y(t)} (4.91) where ball is the regression

**coefficient**of Y(t2) on ...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