Elements of the Theory of Markov Processes and Their ApplicationsThis graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition. |
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Page 1
... model . When formulating a mathematical model , we can select one of two approaches to the study of the phenomenon concerned . These two approaches , which are termed deterministic and stochastic ( or proba- bilistic ) , reflect the ...
... model . When formulating a mathematical model , we can select one of two approaches to the study of the phenomenon concerned . These two approaches , which are termed deterministic and stochastic ( or proba- bilistic ) , reflect the ...
Page 2
... stochastic analogue . Let the function x ( t ) , real - valued and continuous , denote the num- ber of bacteria in a population at time t . To describe the growth of the population , we must formulate a model based on some postulated ...
... stochastic analogue . Let the function x ( t ) , real - valued and continuous , denote the num- ber of bacteria in a population at time t . To describe the growth of the population , we must formulate a model based on some postulated ...
Page 3
... model is a special case of a stochastic model , in the sense that it yields results which hold with probability one . х We close this brief discussion of deterministic and stochastic models by considering the mean or expected population ...
... model is a special case of a stochastic model , in the sense that it yields results which hold with probability one . х We close this brief discussion of deterministic and stochastic models by considering the mean or expected population ...
Page 4
... stochastic process " refers to the mathematical abstraction , model , or representation of the empirical process and not to the empirical process itself . In the example given above , the empirical process involved was the growth of a ...
... stochastic process " refers to the mathematical abstraction , model , or representation of the empirical process and not to the empirical process itself . In the example given above , the empirical process involved was the growth of a ...
Page 9
... model of a discrete branching process can be thought of as a representation ... stochastic processes , together with their interpretation for branching ... stochastic processes is to determine conditions for which the random variable Xn ...
... model of a discrete branching process can be thought of as a representation ... stochastic processes , together with their interpretation for branching ... stochastic processes is to determine conditions for which the random variable Xn ...
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Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |
Common terms and phrases
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 deterministic differential equation diffusion equations diffusion processes distribution function E₁ E₂ electron-photon cascades epidemic expression Feller finite fluctuation problem functional equation given Hence initial condition integral equation interval 0,t ionization Jánossy Kendall Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform Messel 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