## 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 199

This equation, together with some initial condition (the number of infected, or

susceptible, individuals at the start of the

In assuming a deterministic causal mechanism for the spread or development of

the ...

This equation, together with some initial condition (the number of infected, or

susceptible, individuals at the start of the

**epidemic**), is then solved to obtain x(t).In assuming a deterministic causal mechanism for the spread or development of

the ...

Page 205

The stochastic

analogue of the following deterministic model: Consider a homogeneous

population of n individuals, and let z(t) represent the number of susceptibles at

time t, y (t) ...

The stochastic

**epidemic**model characterized by Eq. (4.123) is the stochasticanalogue of the following deterministic model: Consider a homogeneous

population of n individuals, and let z(t) represent the number of susceptibles at

time t, y (t) ...

Page 208

The following relations obtain for the probability of no

n(l — j) ^ p < n (c) 777 = 1 for p ^ n These results have the following

interpretations: If p ^ n, then the probability of an

preassigned ...

The following relations obtain for the probability of no

**epidemic**: for p < n(l — j) forn(l — j) ^ p < n (c) 777 = 1 for p ^ n These results have the following

interpretations: If p ^ n, then the probability of an

**epidemic**exceeding anypreassigned ...

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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