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 12
... matrix of transition probabilities : Poo Po1 Po2 P10 P11 P12 P = P20 P21 P22 ∞ j = 0 - 1 Clearly P is a square matrix ( of infinite order since the chain has a denumerable number of states ) with nonnegative elements , since pis 0 for ...
... matrix of transition probabilities : Poo Po1 Po2 P10 P11 P12 P = P20 P21 P22 ∞ j = 0 - 1 Clearly P is a square matrix ( of infinite order since the chain has a denumerable number of states ) with nonnegative elements , since pis 0 for ...
Page 14
... matrix associated with a decomposable chain can be written in the form of a partitioned matrix ; for example , 2 P = P1 0 0 P2 In the above , P1 and P2 represent Markov matrices which describe the transitions within the two closed sets ...
... matrix associated with a decomposable chain can be written in the form of a partitioned matrix ; for example , 2 P = P1 0 0 P2 In the above , P1 and P2 represent Markov matrices which describe the transitions within the two closed sets ...
Page 35
... matrix II when the matrix of transition probabilities P is given has been considered by many investigators using different methods ( cf. [ 17 ] ) . For the application of semigroup theory to this problem we refer to the paper of Kendall ...
... matrix II when the matrix of transition probabilities P is given has been considered by many investigators using different methods ( cf. [ 17 ] ) . For the application of semigroup theory to this problem we refer to the paper of Kendall ...
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