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 2
... functional equation for X ( t ) ; instead , we attempt to find an expression for the probability that at time t the population size is equal to x . Hence , we seek Px ( t ) P { X ( t ) = x } . = To formulate the stochastic model , we ...
... functional equation for X ( t ) ; instead , we attempt to find an expression for the probability that at time t the population size is equal to x . Hence , we seek Px ( t ) P { X ( t ) = x } . = To formulate the stochastic model , we ...
Page 13
... equation in matrix form becomes pm + n pm pn = ( 1.11 ) Equation ( 1.11 ) is the matrix form of the Chapman - Kolmogorov functional equation . This functional equation , which characterizes Markov chains , is of fundamental importance ...
... equation in matrix form becomes pm + n pm pn = ( 1.11 ) Equation ( 1.11 ) is the matrix form of the Chapman - Kolmogorov functional equation . This functional equation , which characterizes Markov chains , is of fundamental importance ...
Page 24
... functional equation F ( s ) = s . In this section we shall present one proof of this theorem . The proof we give is based on the fixed points of the function F ( s ) ; hence , we shall first give a brief discussion of functional ...
... functional equation F ( s ) = s . In this section we shall present one proof of this theorem . The proof we give is based on the fixed points of the function F ( s ) ; hence , we shall first give a brief discussion of functional ...
Page 38
... functional equation satisfied by G ( s ) , we utilize a classical result due to Königs [ 48 ] : 1 If the function 0 ... functional equation [ 0 ( 8 ) ] = ag ( s ) and the conditions ( 80 ) = 0 , ' ( 80 ) = 1 . : - In applying Königs ...
... functional equation satisfied by G ( s ) , we utilize a classical result due to Königs [ 48 ] : 1 If the function 0 ... functional equation [ 0 ( 8 ) ] = ag ( s ) and the conditions ( 80 ) = 0 , ' ( 80 ) = 1 . : - In applying Königs ...
Page 39
... function F ( s ) and will assume a number of forms depending on the expected value m . A special case was studied by ... functional equation F [ ( 1 − § ) ¥ ( 7 ) + § ] = ( 1 − § ) w ( MT ) + § [ 0,1 ) is the root of F ( s ) = s and y ...
... function F ( s ) and will assume a number of forms depending on the expected value m . A special case was studied by ... functional equation F [ ( 1 − § ) ¥ ( 7 ) + § ] = ( 1 − § ) w ( MT ) + § [ 0,1 ) is the root of F ( s ) = s and y ...
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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