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Article Dans Une Revue Stochastics and Stochastics Reports Année : 2017

Continuity of the Feynman-Kac formula for a generalized parabolic equation

Résumé

It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an extension of the Feynman-Kac formula to semilinear PDEs, see also Pardoux and Rascanu [14]. This method was applied to the class of PDEs with a nonlinear Neumann boundary condition first by Pardoux and Zhang [15]. However, the proof of continuity of the extended Feynman-Kac formula with respect to x (resp. to (t,x)) is not correct in that paper. Here we consider a more general situation, where both the equation and the boundary condition involve the (possibly multivalued) gradient of a convex function. We prove the required continuity. The result for the class of equations studied in [15] is a Corollary of our main results.

Dates et versions

hal-01267325 , version 1 (04-02-2016)

Identifiants

Citer

Etienne Pardoux, Aurel Rascanu. Continuity of the Feynman-Kac formula for a generalized parabolic equation. Stochastics and Stochastics Reports, 2017, 89, pp.726-752. ⟨10.1080/17442508.2016.1276911⟩. ⟨hal-01267325⟩
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