## 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 a (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 ar(t) represent the number of susceptibles at

timet, 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 ar(t) represent the number of susceptibles at

timet, y(t) ...

Page 208

for n(1 — j) < p < n 70 (c) try = 1 for p > n These results have the following

interpretations: If p > m, then the probability of an

preassigned intensity i is zero, while if p < n, the probability of an

small, ...

for n(1 — j) < p < n 70 (c) try = 1 for p > n These results have the following

interpretations: If p > m, then the probability of an

**epidemic**exceeding anypreassigned intensity i is zero, while if p < n, the probability of an

**epidemic**, for ismall, ...

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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