## 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 170

2 we have 6{X(t)} = e->U) (4.4) 9*{X(t)} = e-2"" f '[A(t) + fi(r)ylT) dr (4.5) Jo Hence,

for given X(t) and fi(t) the above yield explicit

variance of X(t). In the special case when A(<) and f*(t) are independent of time

we ...

2 we have 6{X(t)} = e->U) (4.4) 9*{X(t)} = e-2"" f '[A(t) + fi(r)ylT) dr (4.5) Jo Hence,

for given X(t) and fi(t) the above yield explicit

**expressions**for the mean andvariance of X(t). In the special case when A(<) and f*(t) are independent of time

we ...

Page 203

+ Hxtfy*"-*1" (4.118) From (4.118) a formal

obtained by differentiation; that is, m(f) = *{X(t)} = ?f\ OS J»=l +d±] U*~hm (4119)

From (4.119) the epidemic curve, given by — , can be obtained. Hence " dt dm(t) '

^L . .

+ Hxtfy*"-*1" (4.118) From (4.118) a formal

**expression**for the mean can beobtained by differentiation; that is, m(f) = *{X(t)} = ?f\ OS J»=l +d±] U*~hm (4119)

From (4.119) the epidemic curve, given by — , can be obtained. Hence " dt dm(t) '

^L . .

Page 330

... the above

the

neutron to be decreased from the fission energy E0 to the thermal energy Eft

obtained ...

... the above

**expression**becomes The above**expression**can be compared withthe

**expression**for the total time, say T, required for the energy of a sourceneutron to be decreased from the fission energy E0 to the thermal energy Eft

obtained ...

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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