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A stability property of the stochastic heat equation

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  • Ubøe, Jan
  • Zhang, Tusheng

Abstract

In this paper we consider continuity properties of a stochastic heat equation of the form [not partial differential]u(t,x)/[not partial differential]t = [not partial differential]2u(t,x)/[not partial differential]x2 + f(u(t,x))Wx,t. We prove that the solutions of this equation depend continuously on the function f and give some new estimates for this connection.

Suggested Citation

  • Ubøe, Jan & Zhang, Tusheng, 1995. "A stability property of the stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 247-260, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:247-260
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    References listed on IDEAS

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    1. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
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    Cited by:

    1. Anh, V. V. & Leonenko, N. N., 1999. "Non-Gaussian scenarios for the heat equation with singular initial conditions," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 91-114, November.

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