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 97
... integral equation ( 2.178 ) for my ( t ) , the variance of X ( t ) can be obtained , since D2 { X ( t ) } m2 ( t ) + m1 ( t ) - [ m , ( t ) ] 2 . = It is of interest to note that the equations for the moments are integral equations of ...
... integral equation ( 2.178 ) for my ( t ) , the variance of X ( t ) can be obtained , since D2 { X ( t ) } m2 ( t ) + m1 ( t ) - [ m , ( t ) ] 2 . = It is of interest to note that the equations for the moments are integral equations of ...
Page 101
... integral equation can be reduced to the differential equation OF ( 8 , t ) λy F2 ( s , t ) − { x + 2 [ 1 − ( ß − y ) ] } F ( 8 , t ) = Ət - - - + a + 2 ( 1 − B ) + a ( s — 1 ) e - 1t ( 2.196 ) - · A solution of this nonlinear and ...
... integral equation can be reduced to the differential equation OF ( 8 , t ) λy F2 ( s , t ) − { x + 2 [ 1 − ( ß − y ) ] } F ( 8 , t ) = Ət - - - + a + 2 ( 1 − B ) + a ( s — 1 ) e - 1t ( 2.196 ) - · A solution of this nonlinear and ...
Page 273
... integral equation G ( e , z ; t ) = 0 00 = [ ' - ' - " [ " [ " G ( = 2 ; 7 ) & ( 2 1 = , 7 ) w ( e ' , e " ) de ' de " dr ( 5.128 ) 0 z ; 2 , Now let S ( e , t ) denote the kth factorial moment of ( e , n ; t ) . Jánossy has shown that ...
... integral equation G ( e , z ; t ) = 0 00 = [ ' - ' - " [ " [ " G ( = 2 ; 7 ) & ( 2 1 = , 7 ) w ( e ' , e " ) de ' de " dr ( 5.128 ) 0 z ; 2 , Now let S ( e , t ) denote the kth factorial moment of ( e , n ; t ) . Jánossy has shown that ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
13 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 |
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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