A (rough) Pathwise Approach to Fully Non-linear Stochastic Partial Differential Equations
نویسندگان
چکیده
In a series of papers, starting with [Fully nonlinear stochastic partial di¤erential equations. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 9] Lions and Souganidis proposed a (pathwise) theory for fully non-linear stochastic partial di¤erential equations. We present here a (partial) extension towards certain spatial dependence in the noise term. The main novelty is the use of rough path theory in this context [Lyons, Terry J.; Di¤erential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998), no. 2, 215310].
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