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Stochastic heat equation with random coefficients
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  • Published: August 1999

Stochastic heat equation with random coefficients

  • Elisa Alòs1,
  • Jorge A. León2 &
  • David Nualart1 

Probability Theory and Related Fields volume 115, pages 41–94 (1999)Cite this article

Abstract.

We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the Skorohod integral deduced from Itô's formula for this anticipating stochastic integral.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain. e-mail: ealos@porthos.bio.ub.es, , , , , , ES

    Elisa Alòs & David Nualart

  2. Departamento de Matemáticas, CINVESTAV-IPN, Apartado Postal 14-740, 07000 México, , , , , , MX

    Jorge A. León

Authors
  1. Elisa Alòs
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  2. Jorge A. León
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  3. David Nualart
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Additional information

Received: 21 November 1997 / Revised version: 20 July 1998

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Alòs, E., León, J. & Nualart, D. Stochastic heat equation with random coefficients. Probab Theory Relat Fields 115, 41–94 (1999). https://doi.org/10.1007/s004400050236

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  • Issue Date: August 1999

  • DOI: https://doi.org/10.1007/s004400050236

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  • Mathematics Subject Classification (1991): 60H15, 60H07
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