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 = Пі M1 . Now p → π ,; hence , ( 1.61 ) holds for i = j . For any fixed i we ... finite , number of terms yields the inequalities ∞ π ; > ΣπεΡεί k = 0 ( 1.62 ) If we sum the above inequalities over ...
... finite mean recurrence times M ,. Let = Пі M1 . Now p → π ,; hence , ( 1.61 ) holds for i = j . For any fixed i we ... finite , number of terms yields the inequalities ∞ π ; > ΣπεΡεί k = 0 ( 1.62 ) If we sum the above inequalities over ...
Page 267
... Finite Absorber . In this section we consider the fundamental equations for nucleon cascades in homo- geneous nuclear matter and in a finite absorber . A nucleon cascade developing within nuclear matter is called a cascade in ...
... Finite Absorber . In this section we consider the fundamental equations for nucleon cascades in homo- geneous nuclear matter and in a finite absorber . A nucleon cascade developing within nuclear matter is called a cascade in ...
Page 399
... Finite Number of Channels . The Non - Markovian Case : 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 : 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 ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
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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 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 deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function E₁ electron-photon cascades energy epidemic exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon number of individuals o(At obtain P₁ photon Poisson process population probability distribution problem Proc product density queueing system r₁ radiation Ramakrishnan random variable random variable X(t random walk recurrent satisfies sequence Statist stochastic model Stochastic Processes t₁ t₂ Takács tion transition probabilities X₁ zero дх