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            <title xml:lang="en">Continuity of the Feynman-Kac formula for a generalized parabolic equation</title>
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                <forename type="first">Etienne</forename>
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                <title xml:lang="en">Continuity of the Feynman-Kac formula for a generalized parabolic equation</title>
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                    <forename type="first">Etienne</forename>
                    <surname>Pardoux</surname>
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                    <forename type="first">Aurel</forename>
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                  <biblScope unit="volume">89</biblScope>
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              <p>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.</p>
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