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In probabilistic terms Hardy's condition is written as follows: E[e c √ X ] < ∞, where X is a nonnegative random variable and c > 0 a constant. If this holds, then all moments of X are finite and the distribution of X is uniquely determined by the moments. This condition, based on two papers by G. H. Hardy (1917/1918), is weaker than Cramér's condition(More)
Keywords: Hamburger moment problem Powers and products of random variables Carleman's condition Cramér's condition Hardy's condition Krein's condition Normal distribution Laplace distribution Double generalized gamma distribution Logistic distribution a b s t r a c t We present new results on the Hamburger moment problem for probability distributions and(More)
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