## 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. |

### From inside the book

Results 1-3 of 47

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 sn in [G>(a)]\ Thus n qtn = 2 ^{-^1 = *}^ {°f producing a total of n — iindividuals in ...

Page 196

From (4.89) we have &j.i = e*('«-f>) (4.92) hence the correlation

between 7(^) and Y(t2) is given by Hence, except when tl is small, the correlation

that ...

From (4.89) we have &j.i = e*('«-f>) (4.92) hence the correlation

**coefficient**pbetween 7(^) and Y(t2) is given by Hence, except when tl is small, the correlation

**coefficient**is approximately one for all t2 > tv In view of this result we can statethat ...

Page 413

and the

r, n//.) 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-l,r,ril) (9130) ...

and the

**coefficient**of loss for repairmen, which is r-b = j _ S{m-l.r,MH) {Q m) r S(m,r, n//.) 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-l,r,ril) (9130) ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preface | 1 |

Processes Continuous In Space and Time | 3 |

Processes Discrete in Space and Time | 9 |

Copyright | |

10 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 Acad applications assume assumptions asymptotic birth process birth-and-death process cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function electron-photon cascades epidemic exists expression extinction Feller finite fluctuation functional equation gambler's ruin given Hence independent initial condition integral equation interval introduce ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random limit theorems machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon nucleon cascades number of individuals o(At obtain photon Poisson process population positive probability distribution problem Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t random walk recurrent refer satisfies sequence Statist stochastic model Stochastic Processes tion transition probabilities zero