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. |
From inside the book
Results 1-3 of 32
Page 19
... number of individuals in the nth generation , given that X1 = 1 , is = = F ( 8 ) FFn - 1 ( 8 ) ] - ( 1.30 ) where F1 ... number of offsprings of each of the X1 individuals of the first generation is a random variable S1 , say , with ...
... number of individuals in the nth generation , given that X1 = 1 , is = = F ( 8 ) FFn - 1 ( 8 ) ] - ( 1.30 ) where F1 ... number of offsprings of each of the X1 individuals of the first generation is a random variable S1 , say , with ...
Page 42
... number of individuals in all generations . We have already shown ( Sec . 1.4 ) that , when m≤ 1 , the random ... number of individuals in the ( k + 1 ) st generation starting from the ( zero ) th . Put Z = 1 + Y , so Yx = X1 + ··· + X ...
... number of individuals in all generations . We have already shown ( Sec . 1.4 ) that , when m≤ 1 , the random ... number of individuals in the ( k + 1 ) st generation starting from the ( zero ) th . Put Z = 1 + Y , so Yx = X1 + ··· + X ...
Page 48
... number of individuals in the population in the nth generation . The component scalar random variables Xin ( i = 1 , 2 , . . . , N ) represent the number of individuals of the ith type in the nth generation . In the one - dimensional ...
... number of individuals in the population in the nth generation . The component scalar random variables Xin ( i = 1 , 2 , . . . , N ) represent the number of individuals of the ith type in the nth generation . In the one - dimensional ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
13 other sections not shown
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 |
Common terms and phrases
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