## 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. |

### From inside the book

Results 1-3 of 32

Page 136

C. Singular

applications we encounter equations such that a(x) vanishes at one (or possibly ...

C. Singular

**Diffusion Equations**. In most physical applications of the Kolmogorov**diffusion equations**the coefficient a(x) is essentially positive. However, in certainapplications we encounter equations such that a(x) vanishes at one (or possibly ...

Page 138

where An,Bn, and Xn are determined by the initial and boundary conditions

which must be specified for any particular diffusion problem. We now consider

the application of the Laplace transformation1 to the Kolmogorov

where An,Bn, and Xn are determined by the initial and boundary conditions

which must be specified for any particular diffusion problem. We now consider

the application of the Laplace transformation1 to the Kolmogorov

**diffusion****equations**.Page 214

3 we observed that the general description of the forward aspects of a

process is given by the system of

frequency x0 suppressed, is the probability density ofthe gene frequency, and to^

O.* ...

3 we observed that the general description of the forward aspects of a

**diffusion**process is given by the system of

**equations**In the above, f(t,x), with the initialfrequency x0 suppressed, is the probability density ofthe gene frequency, and to^

O.* ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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