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On the positive correlations in Wiener space via fractional calculus. (English) Zbl 1234.60021

Editorial remark: This paper is almost identical with the author’s article [Int. Math. Forum 5, No. 61-64, 3193–3201 (2010; Zbl 1234.60020)]. It has meanwhile been retracted by the editors.

Summary: We study the correlation inequality in the Wiener space using the Malliavin and the fractional calculus. Under positivity and monotonicity conditions, we give a proof of the positive correlation between two random functionals F and G which are assumed smooth enough. The main argument is the Itô-Clark representation formula for the functionals of a fractional Brownian motion.

60E15Inequalities in probability theory; stochastic orderings
60H07Stochastic calculus of variations and the Malliavin calculus
60G22Fractional processes, including fractional Brownian motion