## 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 193

... occur from B to A, we say that a double mutation takes place. Single mutations

are also referred to as forward mutations, while double mutations are called

reverse mutations. Let X(t) and Y(t)

normal) ...

... occur from B to A, we say that a double mutation takes place. Single mutations

are also referred to as forward mutations, while double mutations are called

reverse mutations. Let X(t) and Y(t)

**denote the numbers**of type A organisms (normal) ...

Page 249

The method of product density functions, developed independently by Bhabha [9]

and Ramakrishnan [79], can be described as follows: Let the random variable X(

E;t)

The method of product density functions, developed independently by Bhabha [9]

and Ramakrishnan [79], can be described as follows: Let the random variable X(

E;t)

**denote the number**of particles1 with energy values less than E for arbitrary ...Page 379

When t e T, let the random variable X„ = X(t„ — 0)

customers in the queue after the rath customer has been served. The fact that the

input is Poisson ensures that the imbedded chain is a Markov chain with a

denumerable ...

When t e T, let the random variable X„ = X(t„ — 0)

**denote the number**ofcustomers in the queue after the rath customer has been served. The fact that the

input is Poisson ensures that the imbedded chain is a Markov chain with a

denumerable ...

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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