An Introduction to Probability Theory and Its Applications, Volume 2Wiley, 1950 - Probabilities Vol. 2 has series: Wiley series in probability and mathematical statistics. Bibliographical footnotes. "Some books on cagnate subjects": v. 2, p. 615-616. |
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Page 205
... MARKOV CHAINS The generalization of the discrete Markov chains of 1 ; XV to Cartesian ( and more general ) spaces is rather obvious . In the discrete case the transition probabilities were given by a stochastic matrix with elements Pis ...
... MARKOV CHAINS The generalization of the discrete Markov chains of 1 ; XV to Cartesian ( and more general ) spaces is rather obvious . In the discrete case the transition probabilities were given by a stochastic matrix with elements Pis ...
Page 311
... Markov processes — or rather , of the basic equations governing their transition probabilities . From this we pass to Bochner's notion of subordination of processes and to the treatment of Markov processes by semi - groups . The so ...
... Markov processes — or rather , of the basic equations governing their transition probabilities . From this we pass to Bochner's notion of subordination of processes and to the treatment of Markov processes by semi - groups . The so ...
Page 622
... MARKOV , A. 224 ; property 8 , ( strong 18 ) . - MARKOV processes with continuous time 96 , 311ff . , 586 ; in countable spaces 457 ff .; ergodic thms . 365 , 467 ; in renewal 357 ; - and semi - groups 337 ff ; 429ff . [ Cf. Birth - and ...
... MARKOV , A. 224 ; property 8 , ( strong 18 ) . - MARKOV processes with continuous time 96 , 311ff . , 586 ; in countable spaces 457 ff .; ergodic thms . 365 , 467 ; in renewal 357 ; - and semi - groups 337 ff ; 429ff . [ Cf. Birth - and ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
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An Introduction to Probability Theory and Its Applications, Volume 2 William Feller Limited preview - 1991 |
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a₁ applies arbitrary argument assume asymptotic atoms backward equation Baire functions Borel sets bounded central limit theorem characteristic function common distribution compound Poisson condition consider constant continuous function convergence convolution defined definition denote density derived distribution F distribution function equals example exists exponential distribution F{dx finite interval fixed follows formula given hence implies independent random variables inequality infinitely divisible integral integrand Laplace transform law of large left side lemma Let F limit distribution Markov martingale measure mutually independent normal distribution notation o-algebra obvious operator parameter Poisson process positive probabilistic probability distribution problem proof prove random walk renewal epochs renewal equation renewal process S₁ sample space satisfies semi-group sequence shows solution stable distributions stochastic stochastic kernel symmetric T₁ tends theory transition probabilities uniformly unique variance vector X₁ Y₁ zero expectation