  In this paper, we demonstrate the simulation of fundamental solution for the
parabolic equation by the relationship with Ito diffusion. The factorization
and Monte Carlo methods of the fundamental solution are considered. With the
fact that the fundamental solution can be written as a product of the
transition function and the expectation of a bridge path integral, we give an
novel and efficient algorithm to simulate the fundamental solution by
importance sampling method, especially for dealing with the multi-dimensional
case.
