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 m2 ( t ) = K2 | [ m1 ( t − T ) ] 2q ( 7 ) dτ + K1 ∞ S'male - − m2 ( t . T ) q ( T ) dT ( 2.178 ) ... integral in ( 2.178 ) can be evaluated without difficulty . After solving integral equation ( 2.178 ) for m2 ( t ) ...
... integral equation m2 ( t ) = K2 | [ m1 ( t − T ) ] 2q ( 7 ) dτ + K1 ∞ S'male - − m2 ( t . T ) q ( T ) dT ( 2.178 ) ... integral in ( 2.178 ) can be evaluated without difficulty . After solving integral equation ( 2.178 ) for m2 ( t ) ...
Page 101
... integral equation can be reduced to the differential equation ǝF ( s , t ) = - λy F2 ( s , t ) — { a + 2 [ 1 − ( ẞ − y ) ] } F ( s , t ) - - Ət + a + 2 ( 1 − ß ) + a ( s − 1 ) e ̄1t ( 2.196 ) - A solution of this nonlinear and ...
... integral equation can be reduced to the differential equation ǝF ( s , t ) = - λy F2 ( s , t ) — { a + 2 [ 1 − ( ẞ − y ) ] } F ( s , t ) - - Ət + a + 2 ( 1 − ß ) + a ( s − 1 ) e ̄1t ( 2.196 ) - A solution of this nonlinear and ...
Page 273
... integral equation € t Sx ( e , t ) -alt- = 1 k 00 n = 0 S n ( ) de - a < 8- ( 2-7 , 7 ) 10 ( e ' , e ′′ ) de ' de " dr + de TM ( 5.129 ) × Sr - a with So ( e , t ) = 1. If we consider the integral equation for the mean , we have e - alt ...
... integral equation € t Sx ( e , t ) -alt- = 1 k 00 n = 0 S n ( ) de - a < 8- ( 2-7 , 7 ) 10 ( e ' , e ′′ ) de ' de " dr + de TM ( 5.129 ) × Sr - a with So ( e , t ) = 1. If we consider the integral equation for the mean , we have e - alt ...
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