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. |
From inside the book
Results 1-3 of 30
Page 307
... arrival of the ( i - = 0 , 1 , .... . , denote the 1 ) st and ith impulses . i The arrival times form a recurrent process ; hence , the T , are equidis- tributed independent positive random variables . Let G ( t ) = P { T ; < t } denote ...
... arrival of the ( i - = 0 , 1 , .... . , denote the 1 ) st and ith impulses . i The arrival times form a recurrent process ; hence , the T , are equidis- tributed independent positive random variables . Let G ( t ) = P { T ; < t } denote ...
Page 309
... arrival of the next impulse - if the counter is free . Now , the probability of at most x impulses arriving in the interval ( T , T + t ) is 1 P { ( Z ≤t ) * G ( t ) } . We observe that the event { ZT < t } occurs when there is at ...
... arrival of the next impulse - if the counter is free . Now , the probability of at most x impulses arriving in the interval ( T , T + t ) is 1 P { ( Z ≤t ) * G ( t ) } . We observe that the event { ZT < t } occurs when there is at ...
Page 375
... arrival of " customers " at the " counter " where service is provided . Suppose customers arrive at the counter at times t1 , të , . tn ( 0 < t < tą < ··· < t < co ) and let Ttn + 1 - t denote the difference between the t , time of arrival ...
... arrival of " customers " at the " counter " where service is provided . Suppose customers arrive at the counter at times t1 , të , . tn ( 0 < t < tą < ··· < t < co ) and let Ttn + 1 - t denote the difference between the t , time of arrival ...
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 |
Common terms and phrases
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