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 77
... of the velocity are mutually This section treats a special topic and is not used in the sequel . independent random variables with zero expectation . Applied to rotations III.4 77 A CHARACTERIZATION OF THE NORMAL DISTRIBUTION.
... of the velocity are mutually This section treats a special topic and is not used in the sequel . independent random variables with zero expectation . Applied to rotations III.4 77 A CHARACTERIZATION OF THE NORMAL DISTRIBUTION.
Page 498
... trick is frequently useful . This section treats special topics and is not used in the following text . Proof of the lemma . For all complex and real 498 XV.8 CHARACTERISTIC FUNCTIONS *8 Two Characterizations of the Normal Distribution.
... trick is frequently useful . This section treats special topics and is not used in the following text . Proof of the lemma . For all complex and real 498 XV.8 CHARACTERISTIC FUNCTIONS *8 Two Characterizations of the Normal Distribution.
Page 544
... distribution . ( ii ) If a < 2 and ( 5.6 ) 1 - F ( x ) F ( -x ) P , q 1- F ... normal distribution iff μ is slowly varying . ( This is the case whenever a ... distributions without variance [ 544 XVII.5 INFINITELY DIVISIBLE DISTRIBUTIONS.
... distribution . ( ii ) If a < 2 and ( 5.6 ) 1 - F ( x ) F ( -x ) P , q 1- F ... normal distribution iff μ is slowly varying . ( This is the case whenever a ... distributions without variance [ 544 XVII.5 INFINITELY DIVISIBLE DISTRIBUTIONS.
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