Stochastic representations of derivatives of solutions of one dimensional parabolic variational inequalities with Neumann boundary conditions

Mireille Bossy 1, * Mamadou Cissé 2 Denis Talay 1
* Corresponding author
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : In this paper we explicit the derivative of the flows of one dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.
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Mireille Bossy, Mamadou Cissé, Denis Talay. Stochastic representations of derivatives of solutions of one dimensional parabolic variational inequalities with Neumann boundary conditions. [Research Report] RR-6921, INRIA. 2009, pp.45. ⟨inria-00381854v4⟩

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