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Almost sure approximation of Wong-Zakai type for stochastic partial differential equations

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  • Brzezniak, Zdzislaw
  • Flandoli, Franco

Abstract

A solution to a stochastic partial differential equation (in the Stratonovitch form) is an almost sure limit of solutions to a sequence of approximated equations (with Brownian path w(t) being replaced by a piecewise smooth path wn(t) approximating w(t)). This is achieved by employing a generalized Feynman-Kac formula of Pardoux and Rozovskii and proving the corresponding result for ordinary stochastic differential equations. Parabolic and hyperbolic (degenerate parabolic) evolution equations are studied.

Suggested Citation

  • Brzezniak, Zdzislaw & Flandoli, Franco, 1995. "Almost sure approximation of Wong-Zakai type for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 329-358, February.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:2:p:329-358
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