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 146
... symmetric distribution ° F given by ( 5.2 ) ° F = FF . Using the symmetry property ° F ( x ) = 1 — ° F ( −x ) it is ... symmetric , but not the result of a symmetrization procedure . ( c ) Let F be atomic , attributing weights 146 V.5 ...
... symmetric distribution ° F given by ( 5.2 ) ° F = FF . Using the symmetry property ° F ( x ) = 1 — ° F ( −x ) it is ... symmetric , but not the result of a symmetrization procedure . ( c ) Let F be atomic , attributing weights 146 V.5 ...
Page 166
... symmetric stable R. We start from the simple remark that Sm + n is the sum of the independent variables S , and Sm + n - Sm distributed , respectively , as cX and c , X . Thus for symmetric stable distributions ( 1.3 ) m rk Cm + nX ...
... symmetric stable R. We start from the simple remark that Sm + n is the sum of the independent variables S , and Sm + n - Sm distributed , respectively , as cX and c , X . Thus for symmetric stable distributions ( 1.3 ) m rk Cm + nX ...
Page 171
... symmetric stable distribution with exponent 3. It will turn out that ( up to the trivial scale parameter ) there exists exactly one such distribution , and so we have solved our problem without appeal to deeper theory . The astronomer ...
... symmetric stable distribution with exponent 3. It will turn out that ( up to the trivial scale parameter ) there exists exactly one such distribution , and so we have solved our problem without appeal to deeper theory . The astronomer ...
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