Lower bounds for densities of uniformly elliptic random variables on Wiener space

In this article, we generalize the lower bound estimates for uniformly elliptic di#usion processes obtained by Kusuoka and Stroock. We define the concept of uniform elliptic random variable on Wiener space and show that with this definition one can prove a lower bound estimate of Gaussian type for its density. We apply our results to the case of the stochastic heat equation under the hypothesis of unifom ellipticity of the di#usion coe#cient.