GAUSSIAN INTEGRALS ON WIENER-SPACES

We consider integrals on Wiener space of the forms E(exp K(x)) and E(exp K(x)\L(x) = 1) where K is a quadratic form and L a system of linear forms. We give explicit formulas for these integrals in terms of the operators K and L, in the case that these arise from quasilinear functions in the sense of Zhao (1981). As examples, we recover Levy's area formula in the plane, and derive new formulas for the probability density of the radius of gyration tensor for Brownian paths.