## 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 76

Page 52

Show that the generating function F(s)

condition |F(«2) — < K |«2 — with K < 1, is a contraction mapping; and therefore,

the sequence a0, «t = F(s0), a2 = . . . converges to the single root of the equation

...

Show that the generating function F(s)

**defined**in [0,1] and satisfying theLipschitzcondition |F(«2) — < K |«2 — with K < 1, is a contraction mapping; and therefore,

the sequence a0, «t = F(s0), a2 = . . . converges to the single root of the equation

...

Page 211

4. Age-dependent Branching Processes and Epidemic Models.1 Three important

factors associated with any infectious disease are (1) the latent period, (2) the

infectious period, and (3) the incubation period. The latent period is

the ...

4. Age-dependent Branching Processes and Epidemic Models.1 Three important

factors associated with any infectious disease are (1) the latent period, (2) the

infectious period, and (3) the incubation period. The latent period is

**defined**asthe ...

Page 413

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

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 machineswaiting 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