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 43
... ( coefficient of s ” - in [ 8Gx - 1 ( 8 ) ] ' ) coefficient of 8 " in Σ P [ 8Gx- i = 1 coefficient of 8 " in P , [ SG , ( Σ PdeG2 - 1 ( 0 ) ) \ i = 0 = coefficient of 8 " in F [ 8Gx - 1 ( 8 ) ] Therefore k 00 G2 ( s ) = Σ Ix , n8 ′′ = F ...
... ( coefficient of s ” - in [ 8Gx - 1 ( 8 ) ] ' ) coefficient of 8 " in Σ P [ 8Gx- i = 1 coefficient of 8 " in P , [ SG , ( Σ PdeG2 - 1 ( 0 ) ) \ i = 0 = coefficient of 8 " in F [ 8Gx - 1 ( 8 ) ] Therefore k 00 G2 ( s ) = Σ Ix , n8 ′′ = F ...
Page 196
... coefficient of Y ( t2 ) on Y ( t ) . From ( 4.89 ) we have b2.1 = = ea ( tg - t1 ) ( 4.92 ) hence the correlation coefficient p between Y ( t1 ) and Y ( t2 ) is given by p2 = [ & { Y ( t2 ) [ Y ( t1 ) — & { Y ( t1 ) } ] } ] 2 = 1 1 D2 ...
... coefficient of Y ( t2 ) on Y ( t ) . From ( 4.89 ) we have b2.1 = = ea ( tg - t1 ) ( 4.92 ) hence the correlation coefficient p between Y ( t1 ) and Y ( t2 ) is given by p2 = [ & { Y ( t2 ) [ Y ( t1 ) — & { Y ( t1 ) } ] } ] 2 = 1 1 D2 ...
Page 413
... coefficient of loss for repairmen . ( 9.130 ) For machines , three coefficients of loss are defined . The coefficient of normal loss due to repairs is given by b m - ( rS ( m ― 1 , r , μ / 2 ) ( 9.131 ) m S ( m , r , μ / 2 ) The ...
... coefficient of loss for repairmen . ( 9.130 ) For machines , three coefficients of loss are defined . The coefficient of normal loss due to repairs is given by b m - ( rS ( m ― 1 , r , μ / 2 ) ( 9.131 ) m S ( m , r , μ / 2 ) The ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
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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 applications assume assumptions asymptotic birth process birth-and-death process boundary branching processes cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function E₁ electron-photon cascades energy epidemic exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon number of individuals o(At obtain P₁ photon Poisson process population probability distribution problem Proc product density queueing system r₁ radiation Ramakrishnan random variable random variable X(t random walk recurrent satisfies sequence Statist stochastic model Stochastic Processes t₁ t₂ Takács tion transition probabilities X₁ zero дх