Density Formula in Malliavin Calculus by Using Stein’s Method and Diffusions - Hyun-Suk Park (Mathematics)
Let G be a random variable of functionals of an isonormal Gaussian process X defined on some probability space. Studies have been conducted to determine the exact form of the density function of the random variable G. In this paper, unlike previous studies, we will use the Stein’s method for invariant measures of diffusions to obtain the density formula of G. By comparing the density function obtained in this paper with that of the diffusion invariant measure, we find that the diffusion coefficient of an Itô diffusion with an invariant measure having a density can be expressed as in terms of operators in Malliavin calculus.