## 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 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 ...

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 [$*(«)]'. Thus n qtin = 2 ^{-^1 = *}^* {°f producing a total of n — iindividuals ...

Page 196

i)(e«<'«-'i' - 1) a = ^ [(*„ + yo)^'"1 - ft] [«^"",~',, - '"^l (4-9°) a From (4.89) we observe

that the regression of Y(t2) on 7(<1) is linear; hence, /{r<y[r(y - /{rw}]} = Vi^Wx)}

where 6ai is the regression

i)(e«<'«-'i' - 1) a = ^ [(*„ + yo)^'"1 - ft] [«^"",~',, - '"^l (4-9°) a From (4.89) we observe

that the regression of Y(t2) on 7(<1) is linear; hence, /{r<y[r(y - /{rw}]} = Vi^Wx)}

where 6ai is the regression

**coefficient**of Y(tt) on r(^).Page 413

and the

w, r, The operative efficiency is defined as the ratio of the number of machines

waiting to be serviced to the number of repairmen; hence, 6 = S(m-l,r, g/A) (913Q)

r > ...

and the

**coefficient**of loss for repairmen, which is r-b = j _ 8(m - 1, r, g/A) (g ^ r iS(w, r, The operative efficiency is defined as the ratio of the number of machines

waiting to be serviced to the number of repairmen; hence, 6 = S(m-l,r, g/A) (913Q)

r > ...

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### Contents

Introduction | 1 |

Processes Discrete in Space and Time | 9 |

Processes Discrete in Space and Continuous in Time | 57 |

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 associated assume assumptions asymptotic birth process birth-and-death process branching processes cascade process cascade theory coefficient collision consider defined denote the number denote the probability derive determined deterministic differential equation diffusion equations diffusion processes distribution function electron-photon cascades epidemic exists expression Feller finite fluctuation problem functional equation given Hence initial condition integral equation interval ionization Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random machine Markov chain Markov processes Math mathematical matrix mean and variance mean number Mellin transform Messel method Monte Carlo methods mutation neutron nonnegative nucleon nucleon cascades number of electrons number of individuals o(At obtain parameter photon Phys Poisson process probability distribution Proc Px(t queueing process queueing system radiation Ramakrishnan random variable random variable X(t reaction recurrent refer satisfies solution of Eq Statist stochastic model Stochastic Processes Theorem tion transition probabilities zero