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 73
... assumptions which specify the manner in which the Poisson process develops . Assumptions for the Poisson Process . ( 1 ) The probability of a change in the interval ( t , t + At ) is λ At + o ( At ) , where 2 is a positive constant ...
... assumptions which specify the manner in which the Poisson process develops . Assumptions for the Poisson Process . ( 1 ) The probability of a change in the interval ( t , t + At ) is λ At + o ( At ) , where 2 is a positive constant ...
Page 85
... Assumptions for the Death Process . ( 1 ) At time zero the system is in a state x = x , i.e. , X ( 0 ) = x 。> 1. ( 2 ) If at time t the system is in the statex ( x = 1 , 2 , . . . ) , then the probability of the transition x → x − 1 ...
... Assumptions for the Death Process . ( 1 ) At time zero the system is in a state x = x , i.e. , X ( 0 ) = x 。> 1. ( 2 ) If at time t the system is in the statex ( x = 1 , 2 , . . . ) , then the probability of the transition x → x − 1 ...
Page 412
... assumptions expressed by ( 3 ) to ( 5 ) . In this case , however , it is necessary to modify assumption ( 6 ) . We can therefore conclude that ( 9.123 ) and ( 9.124 ) are valid whenever the limiting probability distribution { m } is ...
... assumptions expressed by ( 3 ) to ( 5 ) . In this case , however , it is necessary to modify assumption ( 6 ) . We can therefore conclude that ( 9.123 ) and ( 9.124 ) are valid whenever the limiting probability distribution { m } is ...
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