Analog of heat equation for Gaussian measure of a ball in Hilbert space
Let \(\mu\) be a Gaussian measure on a separable Hilbert space H with mean vector a and covariance operator T. If g(a,T) is the value of \(\mu\) on a fixed open ball in H, then it is well known that g(,T) is Gateaux differentiable with respect to a. The author proves that g(a,) is also differentiable with respect to all covariance operators T on H and moreover, that the function g(a,T) satisfies the heat equation in a sense which is specified in the paper.
Gaussian measure on a separable Hilbert space
scientific article; zbMATH DE number 4163794
scientific article