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 ix
... Definitions and Properties . 1.3 Calculation of Moments and Cumulants 1.4 The Fundamental Theorem Concerning Branching Processes 1.5 Remarks on the Number of Generations to Extinction 1.6 Limit Theorems • 1.7 Representation as Random ...
... Definitions and Properties . 1.3 Calculation of Moments and Cumulants 1.4 The Fundamental Theorem Concerning Branching Processes 1.5 Remarks on the Number of Generations to Extinction 1.6 Limit Theorems • 1.7 Representation as Random ...
Page 3
... definition m ( t ) = Σ xPx ( t ) = Xeλt x = 0 = ( 0.6 ) Hence , we see that the expression for the mean population ... defined a stochastic process as the mathematical abstraction of an empirical process whose development ( 0.7 ) Since ...
... definition m ( t ) = Σ xPx ( t ) = Xeλt x = 0 = ( 0.6 ) Hence , we see that the expression for the mean population ... defined a stochastic process as the mathematical abstraction of an empirical process whose development ( 0.7 ) Since ...
Page 4
... defining a Markov chain , let us consider the stochastic process studied in classical probability theory , namely , a sequence of independent random variables . Let the random variables X1 , X2 , Xn ( n finite or infinite ) represent ...
... defining a Markov chain , let us consider the stochastic process studied in classical probability theory , namely , a sequence of independent random variables . Let the random variables X1 , X2 , Xn ( n finite or infinite ) represent ...
Page 9
... definitions and properties of this class of stochastic processes , together with their interpretation for branching processes , are given . In Sec . 1.3 the moments and cumulants of the fundamental random variable are studied . A ...
... definitions and properties of this class of stochastic processes , together with their interpretation for branching processes , are given . In Sec . 1.3 the moments and cumulants of the fundamental random variable are studied . A ...
Page 10
... Definitions and Properties A. Discrete Branching Processes and Markov Chains . We consider a stochastic process { Xn , n ... definition of the convolution operation . of the population , i.e. , the population sizes in 10 THEORY OF MARKOV ...
... Definitions and Properties A. Discrete Branching Processes and Markov Chains . We consider a stochastic process { Xn , n ... definition of the convolution operation . of the population , i.e. , the population sizes in 10 THEORY OF MARKOV ...
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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