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 243
... convergence to indicate that the limit F is defective . The following theorem is basic . It restates the definition of convergence in terms of expectations and , at the same time , it provides a criterion for the convergence of a ...
... convergence to indicate that the limit F is defective . The following theorem is basic . It restates the definition of convergence in terms of expectations and , at the same time , it provides a criterion for the convergence of a ...
Page 276
... convergence . If F is a defective distribution then ( 10.1 ) implies that Fn Fimproperly . The converse is not true . Show that proper convergence may be defined by requiring that ( 10.1 ) holds for n ≥ N ( e , h ) , independently of t ...
... convergence . If F is a defective distribution then ( 10.1 ) implies that Fn Fimproperly . The converse is not true . Show that proper convergence may be defined by requiring that ( 10.1 ) holds for n ≥ N ( e , h ) , independently of t ...
Page 481
... convergence → q is uniform in every finite interval . Proof . ( a ) Proper convergence F → F implies the convergence of the corresponding expectations for every bounded continuous function u . For u ( x ) = eix ( and fixed ( ) it ...
... convergence → q is uniform in every finite interval . Proof . ( a ) Proper convergence F → F implies the convergence of the corresponding expectations for every bounded continuous function u . For u ( x ) = eix ( and fixed ( ) it ...
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 |
Common terms and phrases
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