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 61
Albert T. Bharucha-Reid. equation , since it involves differentiation with respect to the earlier time T. 2.3 Infinite Systems of Stochastic Differential Equations A. The Kolgomorov Differential Equations . We now turn from the general ...
Albert T. Bharucha-Reid. equation , since it involves differentiation with respect to the earlier time T. 2.3 Infinite Systems of Stochastic Differential Equations A. The Kolgomorov Differential Equations . We now turn from the general ...
Page 73
Albert T. Bharucha-Reid. each case we derive the differential - difference equation describing the probability law of the process and obtain the solution of the equation and discuss its properties . For the birth and birth - and - death ...
Albert T. Bharucha-Reid. each case we derive the differential - difference equation describing the probability law of the process and obtain the solution of the equation and discuss its properties . For the birth and birth - and - death ...
Page 122
... differential equations for this process , with initial conditions P1 ( 0 ) ... equation for the generating function and apply the bilateral Laplace ... differential equation 2x α ( 22 – 1 ) , με = ǝF ( 8 , t ) at ( 1 8 ) ( as + B ) F ( 8 ...
... differential equations for this process , with initial conditions P1 ( 0 ) ... equation for the generating function and apply the bilateral Laplace ... differential equation 2x α ( 22 – 1 ) , με = ǝF ( 8 , t ) at ( 1 8 ) ( as + B ) F ( 8 ...
Contents
Introduction | 1 |
THEORY | 7 |
Processes Discrete in Space and Continuous in Time | 53 |
Copyright | |
16 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 arrival 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 derive determined deterministic differential equation diffusion equations diffusion processes distribution function E₁ electron electron-photon cascades energy epidemic equilibrium exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization joins the queue Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random limiting distribution Markov chain Markov processes Math matrix Mellin transform Monte Carlo methods nonnegative nucleon o(At obtain P₁ parameter particle photon Phys Poisson process population probability distribution Proc product density queueing process queueing system Ramakrishnan random variable random variable X(t recurrent repairman satisfies Statist stochastic model Stochastic Processes t₁ Takács Theorem tion transition probabilities x₁ zero