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Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs

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1.	Title	Title of document	Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs
2.	Creator	Author's name, affiliation, country	Khaled Bahlali; Université de Toulon (IMATH) and Aix-Marseille Université (CNRS, LATP); France
2.	Creator	Author's name, affiliation, country	Lucian Maticiuc; "Alexandru Ioan Cuza" University of Iasi and “Gheorghe Asachi” Technical University; Romania
2.	Creator	Author's name, affiliation, country	Adrian Zalinescu; "Alexandru Ioan Cuza" University of Iasi and “Octav Mayer” Mathematics Institute of the Romanian Academy; Romania
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Reflecting stochastic differential equation; Penalization method; Weak solution; Jakubowski S-topology; Backward stochastic differential equations
3.	Subject	Subject classification	60H99, 60H30, 35K61
4.	Description	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 the penalized partial differential equation.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-11-27
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2467
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2467
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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