## 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 34

The above is a contradiction; hence, the limit (1.68) must exist for any i and./, and

this completes the proof. CO Theorem 1.8 states that 2 ^ 1 • Foster [20] has given

a classifica-

The above is a contradiction; hence, the limit (1.68) must exist for any i and./, and

this completes the proof. CO Theorem 1.8 states that 2 ^ 1 • Foster [20] has given

a classifica-

**tion**of chains based on the properties of the ir(f. A chain is termed ...Page 154

Let F(s) = 00 2 p(x)«*, \s\ ^ 1, where p(x) is the probability that in the first genera-

*=o

Our purpose is to pass from the generating function associated with the simple ...

Let F(s) = 00 2 p(x)«*, \s\ ^ 1, where p(x) is the probability that in the first genera-

*=o

**tion**x individuals will be formed from a single individual present at time zero.Our purpose is to pass from the generating function associated with the simple ...

Page 227

... volume, the initial damage is transmitted through the system by the chain

depolymeriza-

complete depolymerization of the macromolecules is assumed to be responsible

for ...

... volume, the initial damage is transmitted through the system by the chain

depolymeriza-

**tion**of the macromolecules connected to the control molecule. Thecomplete depolymerization of the macromolecules is assumed to be responsible

for ...

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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