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

• 成果类型: Article
• 署名作者: Kohatsu-Higa, A
• 署名单位: Pompeu Fabra University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0272-4
• 发表日期: 2003
• 页码: 421-457
• 关键词: fundamental-solutions; malliavin calculus; diffusion; PROPERTY

摘要

In this article, we generalize the lower bound estimates for uniformly elliptic diffusion 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 diffusion coefficient.