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 2
... assume ( 1 ) that at time t there are x bacteria in the population and ( 2 ) that the population can only increase in size and that the increase in the interval ( t , t + At ) is proportional to the number of bacteria present at time t ...
... assume ( 1 ) that at time t there are x bacteria in the population and ( 2 ) that the population can only increase in size and that the increase in the interval ( t , t + At ) is proportional to the number of bacteria present at time t ...
Page 48
... assume only integer values , the space X has a lattice structure , with the points x = ( X1 , X2 , representing the possible states of the system . We now assume that an individual of type i ( i = 1 , 2 , ... , N ) in the nth generation ...
... assume only integer values , the space X has a lattice structure , with the points x = ( X1 , X2 , representing the possible states of the system . We now assume that an individual of type i ( i = 1 , 2 , ... , N ) in the nth generation ...
Page 390
... assume that for λu < 1 the limiting distri- bution function F * ( w ) exists , then Eq . ( 9.38 ) can be obtained ... assume that the Poisson parameter λ ( t ) further simplify matters , we assume that W ( 0 ) random variable 0 , denote ...
... assume that for λu < 1 the limiting distri- bution function F * ( w ) exists , then Eq . ( 9.38 ) can be obtained ... assume that the Poisson parameter λ ( t ) further simplify matters , we assume that W ( 0 ) random variable 0 , denote ...
Contents
Introduction | 1 |
THEORY | 7 |
Processes Discrete in Space and Continuous in Time | 53 |
Copyright | |
16 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 arrival 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 derive determined deterministic differential equation diffusion equations diffusion processes distribution function E₁ electron electron-photon cascades energy epidemic equilibrium exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization joins the queue Kendall Kolmogorov equations Laplace transform Laplace-Stieltjes transform Let the random limiting distribution Markov chain Markov processes Math matrix Mellin transform Monte Carlo methods nonnegative nucleon o(At obtain P₁ parameter particle photon Phys Poisson process population probability distribution Proc product density queueing process queueing system Ramakrishnan random variable random variable X(t recurrent repairman satisfies Statist stochastic model Stochastic Processes t₁ Takács Theorem tion transition probabilities x₁ zero