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Fractional integration for irregular martingales (2009.05293v1)
Published 11 Sep 2020 in math.PR and math.CA
Abstract: We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively irregular; the second version lacks the martingale property while being analytically meaningful for an arbitrary filtration.
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