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 45
... Gambler's Ruin and the Problem of Extinction of a Population . We now consider the relationship between the classical gambler's ruin problem and the problem of extinction of a population after ʼn generations . The gambler's ruin problem ...
... Gambler's Ruin and the Problem of Extinction of a Population . We now consider the relationship between the classical gambler's ruin problem and the problem of extinction of a population after ʼn generations . The gambler's ruin problem ...
Page 46
... gambler's ruin problem , it is necessary to consider the case when a = ∞o , that is , the case in which x = 0 is the only absorbing barrier ( or state ) . In this case the boundary conditions ( 1.107 ) are replaced by the single ...
... gambler's ruin problem , it is necessary to consider the case when a = ∞o , that is , the case in which x = 0 is the only absorbing barrier ( or state ) . In this case the boundary conditions ( 1.107 ) are replaced by the single ...
Page 465
... Gambler's ruin problem ) Feller integrodifferential equations , 60 , 120 Feller - Lundberg theorem , 81 , 82 , 91 Final class , 50 First - passage time , 17 , 93 , 148 First - passage time problems , in chemis- try , 371 for diffusion ...
... Gambler's ruin problem ) Feller integrodifferential equations , 60 , 120 Feller - Lundberg theorem , 81 , 82 , 91 Final class , 50 First - passage time , 17 , 93 , 148 First - passage time problems , in chemis- try , 371 for diffusion ...
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