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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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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DOI: https://doi.org/10.1007/s004400050236
- Mathematics Subject Classification (1991): 60H15, 60H07