Lower bounds for densities of uniformly elliptic random variables on Wiener space |
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Authors: | Arturo Kohatsu-Higa |
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Affiliation: | (1) Universitat Pompeu Fabra, Department of Economics, Ramón Trias Fargas 25-27, 08005 Barcelona, Spain. e-mail: kohatsu@upf.es, ES |
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Abstract: | 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.
Received: 6 November 2001 / Revised version: 27 February 2003 /
Published online: 12 May 2003
Key words or phrases: Malliavin Calculus – Density estimates – Aronson estimates |
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