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 193
... denote the numbers of type A organisms ( normal ) and type B organisms ( mutant ) in the population at time t ... number of organisms of type A ( normal form ) in the population at time t and let the random variable Y ( t ) denote the ...
... denote the numbers of type A organisms ( normal ) and type B organisms ( mutant ) in the population at time t ... number of organisms of type A ( normal form ) in the population at time t and let the random variable Y ( t ) denote the ...
Page 249
... denote the number of particles1 with energy values less than E for arbitrary thickness t . Then the random variable dX ( E ; t ) denotes the number of particles in the elementary interval dE . Now let fi ( E ; t ) be a function such ...
... denote the number of particles1 with energy values less than E for arbitrary thickness t . Then the random variable dX ( E ; t ) denotes the number of particles in the elementary interval dE . Now let fi ( E ; t ) be a function such ...
Page 379
... denote the number of customers in the queue after the nth customer has been served . The fact that the input is Poisson ensures that the imbedded chain is a Markov chain with a denumerable number of states . Now let i and j denote the ...
... denote the number of customers in the queue after the nth customer has been served . The fact that the input is Poisson ensures that the imbedded chain is a Markov chain with a denumerable number of states . Now let i and j denote the ...
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