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 73
... assumptions which specify the manner in which the Poisson process develops . Assumptions for the Poisson Process . ( 1 ) The probability of a change in the interval ( t , t + At ) is λ At + o ( At ) , where 2 is a positive constant ...
... assumptions which specify the manner in which the Poisson process develops . Assumptions for the Poisson Process . ( 1 ) The probability of a change in the interval ( t , t + At ) is λ At + o ( At ) , where 2 is a positive constant ...
Page 85
... Assumptions for the Death Process . ( 1 ) At time zero the system is in a state x = x , i.e. , X ( 0 ) = x 。> 1. ( 2 ) If at time t the system is in the statex ( x = 1 , 2 , . . . ) , then the probability of the transition x → x − 1 ...
... Assumptions for the Death Process . ( 1 ) At time zero the system is in a state x = x , i.e. , X ( 0 ) = x 。> 1. ( 2 ) If at time t the system is in the statex ( x = 1 , 2 , . . . ) , then the probability of the transition x → x − 1 ...
Page 266
... assumptions concerning the nucleon - nucleon collisions and the associated cross sections . It is assumed that all ... assumption , which is based on the Heitler - Jánossy theory [ 35 ] , is analogous to the assumption made in the theory ...
... assumptions concerning the nucleon - nucleon collisions and the associated cross sections . It is assumed that all ... assumption , which is based on the Heitler - Jánossy theory [ 35 ] , is analogous to the assumption made in the theory ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
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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 applications assume assumptions asymptotic birth process birth-and-death process boundary branching processes cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function E₁ electron-photon cascades energy epidemic exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon number of individuals o(At obtain P₁ photon Poisson process population probability distribution problem Proc product density queueing system r₁ radiation Ramakrishnan random variable random variable X(t random walk recurrent satisfies sequence Statist stochastic model Stochastic Processes t₁ t₂ Takács tion transition probabilities X₁ zero дх