## 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 5

probability pu,

defined as follows: Pii = &{Xn+1 = E,\Xn = Et} n = 0, 1, . . . (0.9) In addition to the

probabilities ptj, it is necessary to know the probabilities q(j) which give the ...

probability pu,

**associated**with every pair of outcomes or states (E{, Ej), which isdefined as follows: Pii = &{Xn+1 = E,\Xn = Et} n = 0, 1, . . . (0.9) In addition to the

probabilities ptj, it is necessary to know the probabilities q(j) which give the ...

Page 142

In Sec. 3.3B we present some results of Feller [9] on the classification of

boundaries

classification is very important, for it enables us to formulate the correct forward

Kolmogorov equation ...

In Sec. 3.3B we present some results of Feller [9] on the classification of

boundaries

**associated**with one-dimensional diffusion process. Thisclassification is very important, for it enables us to formulate the correct forward

Kolmogorov equation ...

Page 214

In order to characterize the diffusion process

situation, it is necessary to specify the coefficients a(x) and b(x), as well as the

other quantities, which occur in the forward system (4.137). As pointed out in

Chap ...

In order to characterize the diffusion process

**associated**with a given geneticsituation, it is necessary to specify the coefficients a(x) and b(x), as well as the

other quantities, which occur in the forward system (4.137). As pointed out in

Chap ...

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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