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 185
... denote the probability that a single individual will migrate from R1 to R2 in the interval ( t , t + At ) , given that x individuals have migrated in the interval [ 0 , t ) . The function p ( x , t ) is called the migration probability ...
... denote the probability that a single individual will migrate from R1 to R2 in the interval ( t , t + At ) , given that x individuals have migrated in the interval [ 0 , t ) . The function p ( x , t ) is called the migration probability ...
Page 228
... probabilities of recovery and observable damage , respectively . These probabilities can be obtained as follows : Let P , denote the probability of absorption in state n given that the system was initially in state i , i = 1 , 2 ...
... probabilities of recovery and observable damage , respectively . These probabilities can be obtained as follows : Let P , denote the probability of absorption in state n given that the system was initially in state i , i = 1 , 2 ...
Page 349
... denote by 0 ( § ) the probability that the photograph will contain a noticeable image of the galaxy . It is assumed that the function ( § ) is defined for every galaxy , and that is a continuous function for all values of § . @ 2 We now ...
... denote by 0 ( § ) the probability that the photograph will contain a noticeable image of the galaxy . It is assumed that the function ( § ) is defined for every galaxy , and that is a continuous function for all values of § . @ 2 We now ...
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