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. |
From inside the book
Results 1-3 of 82
Page 254
... proof requires only obvious changes . ) Necessary and sufficient conditions for a normal limit are given in IX , 7 . 1 a The method of proof is of wide applicability . Problem 16 may serve as a good exercise . Here we use the method to ...
... proof requires only obvious changes . ) Necessary and sufficient conditions for a normal limit are given in IX , 7 . 1 a The method of proof is of wide applicability . Problem 16 may serve as a good exercise . Here we use the method to ...
Page 421
... Proof . If the first relation in ( 5.12 ) holds then W ( Tλ ) W ( T ) → 0 for λ > a and by the extended continuity ... proof for this special case . ( This proof is still found in texts on complex variables and Laplace transforms ...
... Proof . If the first relation in ( 5.12 ) holds then W ( Tλ ) W ( T ) → 0 for λ > a and by the extended continuity ... proof for this special case . ( This proof is still found in texts on complex variables and Laplace transforms ...
Page 545
... proof . Lemma 2. A distribution F satisfying the conditions of theorem 1 possesses absolute moments of every order ß < a . Proof . Clearly13 as t → ∞ ( 5.15 ) 1 − F ( t ) + F ( −t ) = O ( t − ¤ + ) - for each > 0. The assertion now ...
... proof . Lemma 2. A distribution F satisfying the conditions of theorem 1 possesses absolute moments of every order ß < a . Proof . Clearly13 as t → ∞ ( 5.15 ) 1 − F ( t ) + F ( −t ) = O ( t − ¤ + ) - for each > 0. The assertion now ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
71 other sections not shown
Other editions - View all
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