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Lower bounds for densities of uniformly elliptic random variables on Wiener space
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  • Published: June 2003

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

  • Arturo Kohatsu-Higa1 

Probability Theory and Related Fields volume 126, pages 421–457 (2003)Cite this article

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  • 23 Citations

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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.

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Authors and Affiliations

  1. Universitat Pompeu Fabra, Department of Economics, Ramón Trias Fargas 25-27, 08005 Barcelona, Spain. e-mail: kohatsu@upf.es, , , , , , ES

    Arturo Kohatsu-Higa

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  1. Arturo Kohatsu-Higa
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Additional information

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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Cite this article

Kohatsu-Higa, A. Lower bounds for densities of uniformly elliptic random variables on Wiener space. Probab. Theory Relat. Fields 126, 421–457 (2003). https://doi.org/10.1007/s00440-003-0272-4

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  • Issue Date: June 2003

  • DOI: https://doi.org/10.1007/s00440-003-0272-4

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Keywords

  • Diffusion Coefficient
  • Lower Bound
  • Diffusion Process
  • Heat Equation
  • Gaussian Type
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