Some covariance inequalities in Wiener space (Q999858)

Several covariance inequalities are given on an abstract Wiener space; this enables the authors to give sufficient conditions under which two variables are positively correlated. As a first step, a Taylor-type formula is given for the covariance of two smooth enough variables. Then an inequality is obtained for variables which are increasing with respect to cones of the Cameron-Martin space. The last part is devoted to convex and log-concave variables (the convexity is again with respect to the Cameron-Martin space).