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Journal articles
Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs
Abstract : In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on a penalization method and our approach is probabilistic. We prove the weak uniqueness of the solution for the reflected stochastic differential equation and we approximate it (in law) by a sequence of solutions of stochastic differential equations with penalized terms. Using then a suitable generalized backward stochastic differential equation and the uniqueness of the reflected stochastic differential equation, we prove the existence of a continuous function, given by a probabilistic representation, which is a viscosity solution of the considered partial differential equation. In addition, this solution is approximated by solutions of penalized partial differential equations
Cited literature [22 references]
https://hal-univ-tln.archives-ouvertes.fr/hal-00998298
Contributor : Khaled Bahlali Connect in order to contact the contributor
Submitted on : Sunday, August 30, 2015 - 1:06:48 PM
Last modification on : Tuesday, December 7, 2021 - 3:16:02 PM
Long-term archiving on: : Tuesday, April 11, 2017 - 2:22:15 AM
Contributor : Khaled Bahlali Connect in order to contact the contributor
Submitted on : Sunday, August 30, 2015 - 1:06:48 PM
Last modification on : Tuesday, December 7, 2021 - 3:16:02 PM
Long-term archiving on: : Tuesday, April 11, 2017 - 2:22:15 AM
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