## 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 82

Page 58

associated with the process {X{t), t ^ 0}, that is, X is the space of all possible

values x which the

which is a subset of J, that is, E <=□ X. The probability of the event E is a set

function P{E) ...

associated with the process {X{t), t ^ 0}, that is, X is the space of all possible

values x which the

**random variable X**(**t**) can assume. Denote by E an event,which is a subset of J, that is, E <=□ X. The probability of the event E is a set

function P{E) ...

Page 308

Let the

counter in the interval [0,0 and let P(x,t) = &{X(t) < x) In addition to determining the

above distribution function, we also determine the following probabilities: (a) 9{X{

T + ...

Let the

**random variable X**(**t**) denote the number of impulses arriving at thecounter in the interval [0,0 and let P(x,t) = &{X(t) < x) In addition to determining the

above distribution function, we also determine the following probabilities: (a) 9{X{

T + ...

Page 440

B. Some Theorems and Properties Theorem A.l : The expected value of the

the expected value of X(t) is *{X(t)} = fxPa(t) ior&{X(t)} < oo. By differentiating (A. j),

we ...

B. Some Theorems and Properties Theorem A.l : The expected value of the

**random variable X**[**t**) is given by *{X(t)} = d-?p] (A.3) ds J»=i Proof: By definition,the expected value of X(t) is *{X(t)} = fxPa(t) ior&{X(t)} < oo. By differentiating (A. j),

we ...

### 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