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
... deterministic or stochastic . We are only concerned with the formula- tion of a deterministic or stochastic model , the investigation of its properties , and its ability to account for experimental observations . We remark that the ...
... deterministic or stochastic . We are only concerned with the formula- tion of a deterministic or stochastic model , the investigation of its properties , and its ability to account for experimental observations . We remark that the ...
Page 2
... deterministic solution ( 0.2 ) is that it tells us that , whenever the initial value x 。 is the same , the population size will always be the same for a given time t > 0 . We now consider the stochastic analogue of the above model ...
... deterministic solution ( 0.2 ) is that it tells us that , whenever the initial value x 。 is the same , the population size will always be the same for a given time t > 0 . We now consider the stochastic analogue of the above model ...
Page 3
... deterministic solution ( 0.2 ) shows that , for 2 and xo fixed , we have associated with every value of t a real number x ( t ) . From ( 0.5 ) we see that , for 2 and ≈。 fixed , and for every pair ( x , t ) , x ≥ xo , t > 0 , there ...
... deterministic solution ( 0.2 ) shows that , for 2 and xo fixed , we have associated with every value of t a real number x ( t ) . From ( 0.5 ) we see that , for 2 and ≈。 fixed , and for every pair ( x , t ) , x ≥ xo , t > 0 , there ...
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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 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