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 57
... derive the fundamental integrodifferential equations of Markov processes of this type . These equations are specialized in Sec . 2.3 , where we study the Kolmogorov differential equations . The Kolmogorov equations , which are ...
... derive the fundamental integrodifferential equations of Markov processes of this type . These equations are specialized in Sec . 2.3 , where we study the Kolmogorov differential equations . The Kolmogorov equations , which are ...
Page 60
... derive these equations , we shall utilize the Chapman - Kolmogorov equa- tion and condition ( 2.16 ) . In the Chapman - Kolmogorov equation ( 2.9 ) we put tt + At and 8 = t ; then by using ( 2.16 ) , we have P ( E , tAt ; E , T ) = S ...
... derive these equations , we shall utilize the Chapman - Kolmogorov equa- tion and condition ( 2.16 ) . In the Chapman - Kolmogorov equation ( 2.9 ) we put tt + At and 8 = t ; then by using ( 2.16 ) , we have P ( E , tAt ; E , T ) = S ...
Page 73
... derive the differential equation , it is necessary to state the 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 ...
... derive the differential equation , it is necessary to state the 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 ...
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 Acad applications assume assumptions asymptotic birth process birth-and-death process boundary branching processes cascade process cascade theory coefficients collision consider counter defined denote the number denote the probability derive deterministic differential equation diffusion equations diffusion processes distribution function E₁ electron-photon cascades epidemic expression Feller finite fluctuation problem functional equation given Hence initial condition integral equation interval 0,t ionization Jánossy Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform Messel method Monte Carlo methods neutron nucleon nucleon cascades number of individuals o(At obtain P₁ photon Phys Poisson process population probability distribution Proc queueing process queueing system r₁ r₂ radiation Ramakrishnan random variable random variable X(t recurrent satisfies Statist stochastic model Stochastic Processes t₁ t₂ Takács Theorem tion transition probabilities X₁ zero дх