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 61
Page 173
... INFINITELY DIVISIBLE DISTRIBUTIONS IN R1 Definition 1. A distribution F is infinitely divisible if for every n there exists a distribution F , such that F = Fn . In other words , F is infinitely divisible iff for each n it can be ...
... INFINITELY DIVISIBLE DISTRIBUTIONS IN R1 Definition 1. A distribution F is infinitely divisible if for every n there exists a distribution F , such that F = Fn . In other words , F is infinitely divisible iff for each n it can be ...
Page 534
... infinitely divisible . This proves Theorem 1. For w to be an infinitely divisible characteristic function it is necessary and sufficient that there exist a canonical measure M and a real number b such that ∞ = eo with p of the form ...
... infinitely divisible . This proves Theorem 1. For w to be an infinitely divisible characteristic function it is necessary and sufficient that there exist a canonical measure M and a real number b such that ∞ = eo with p of the form ...
Page 557
... infinitely divisible characteristic function w = e possesses a domain of partial attraction . Indeed , we know that w is the limit of a sequence of characteristic functions we of the compound Poisson type . Define λ by ( 9.3 ) and put ...
... infinitely divisible characteristic function w = e possesses a domain of partial attraction . Indeed , we know that w is the limit of a sequence of characteristic functions we of the compound Poisson type . Define λ by ( 9.3 ) and put ...
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