## 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 182

The probability of a unit increase in the population size of 81 in the interval (t, t +

At),

probability of a unit decrease in the population size of (Sfx in the interval (t, ...

The probability of a unit increase in the population size of 81 in the interval (t, t +

At),

**given**that there are exactly x individuals in Sx at time t, is Xu At + o(At). 2. Theprobability of a unit decrease in the population size of (Sfx in the interval (t, ...

Page 269

Let Hn(E0; El En, t) dE1 dE □ □ • dE„ denote the differential probability that after

a depth t a primary nucleon of energy E0 has

energies in the intervals (Eit Es + dEt), i = 1 , 2, . . . , n. MeBsel and Potts have

shown ...

Let Hn(E0; El En, t) dE1 dE □ □ • dE„ denote the differential probability that after

a depth t a primary nucleon of energy E0 has

**given**rise to n nucleons withenergies in the intervals (Eit Es + dEt), i = 1 , 2, . . . , n. MeBsel and Potts have

shown ...

Page 354

The formal solution of Eq. (7.58) is

<) is the probability that a photon absorbed at a

The formal solution of Eq. (7.58) is

**given**by ... considered by Sobolev.1 Here *&,,(<) is the probability that a photon absorbed at a

**given**point t will be reemitted in a**given**direction p in the radiation emerging from the surface of the atmosphere.### What people are saying - Write a review

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### 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