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 29
... finite mean recurrence times M ,. Let T , = M ; 1 . Now p ( n ) → π ;; hence , ( 1.61 ) holds for ∞ i = j . For ... finite , number of terms yields the inequalities П ; ΣπεΡεί k = 0 ( 1.62 ) If we sum the above inequalities over all k ...
... finite mean recurrence times M ,. Let T , = M ; 1 . Now p ( n ) → π ;; hence , ( 1.61 ) holds for ∞ i = j . For ... finite , number of terms yields the inequalities П ; ΣπεΡεί k = 0 ( 1.62 ) If we sum the above inequalities over all k ...
Page 395
... finite mean recurrence time if ε { n } < & { Tn } . Equation ( 9.60 ) , which is an integral equation of the Wiener - Hopf type , has been solved by Lindley for the case of a queueing system of type D / E / 1 . Its solution has been ...
... finite mean recurrence time if ε { n } < & { Tn } . Equation ( 9.60 ) , which is an integral equation of the Wiener - Hopf type , has been solved by Lindley for the case of a queueing system of type D / E / 1 . Its solution has been ...
Page 399
... Finite Number of Channels . The Non - Markovian Case : 1 Arbitrary Arrival Times and Negative - exponential Holding Times . Let us now consider the equilibrium theory for telephone exchanges with a finite number of states when it is ...
... Finite Number of Channels . The Non - Markovian Case : 1 Arbitrary Arrival Times and Negative - exponential Holding Times . Let us now consider the equilibrium theory for telephone exchanges with a finite number of states when it is ...
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