A CHARACTERIZATION OF PROBABILITY MEASURES IN TERMS OF WICK PRODUCT INEQUALITIES
2008 ◽
Vol 11
(03)
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pp. 377-391
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Keyword(s):
It is known that if X is a normally distributed random variable, and ♢ and E denote the Wick product and expectation, respectively, then for any non-negative integers m and n, and any polynomial functions f and g of degrees at most m and n, respectively, the following inequality holds: [Formula: see text] We show that this result can be extended to a random variable X, not necessary Gaussian, having an infinite support and finite moments of all orders, if and only if its Szegö–Jacobi sequence {ωk}k ≥ 1 is super-additive.
2008 ◽
Vol 2008
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pp. 1-22
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2019 ◽
Vol 22
(02)
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pp. 1950009
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2006 ◽
Vol 462
(2068)
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pp. 1181-1195
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1987 ◽
Vol 24
(04)
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pp. 838-851
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2014 ◽
Vol 17
(03)
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pp. 1450021
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2012 ◽
Vol 43
(3)
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pp. 518-525
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Keyword(s):
1969 ◽
Vol 6
(02)
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pp. 409-418
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1972 ◽
Vol 9
(02)
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pp. 457-461
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