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 58
Albert T. Bharucha-Reid. associated with the process { X ( t ) , t > 0 } , that is , X is the space of all possible values x which the random variable X ( t ) can assume . Denote by E an event , which is a subset of X , that is , EX . The ...
Albert T. Bharucha-Reid. associated with the process { X ( t ) , t > 0 } , that is , X is the space of all possible values x which the random variable X ( t ) can assume . Denote by E an event , which is a subset of X , that is , EX . The ...
Page 121
... t ) ≤ 1 * ... .. Σ j1 = 0 00 ... Σ ... k1 = 0 00 Σ Pij ( T , t ) = 1 IN = 0 ... { X ( t ) , t > 0 } be a time - homogeneous stochastic process with ... random variable X ( t ) , show that F ( 1 / s , t ) is the generating function ...
... t ) ≤ 1 * ... .. Σ j1 = 0 00 ... Σ ... k1 = 0 00 Σ Pij ( T , t ) = 1 IN = 0 ... { X ( t ) , t > 0 } be a time - homogeneous stochastic process with ... random variable X ( t ) , show that F ( 1 / s , t ) is the generating function ...
Page 308
Albert T. Bharucha-Reid. = We now consider the mathematical model for the action of the counter . Put to to and ... random variable X ( t ) denote the number of impulses arriving at the counter in the interval [ 0 , t ) and let P ( x , t ) ...
Albert T. Bharucha-Reid. = We now consider the mathematical model for the action of the counter . Put to to and ... random variable X ( t ) denote the number of impulses arriving at the counter in the interval [ 0 , t ) and let P ( x , t ) ...
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