WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs-Reference-Cited by-同舟云学术

WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs

Published:2008-06 Issue:02 Volume:08 Page:247-269
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

OUKNINE YOUSSEF¹,NDIAYE DJIBRIL²

Affiliation:

1. Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University 2390 Marrakesh, Morocco

2. Laboratoire de Mathématiques Appliquées, Université Cheikh, Anta Diop De Dakar BP 5005 Dakar-Fann, Sénégal

Abstract

We prove the existence and uniqueness of the solution of a semilinear PDEs with obstacle(s) under Lipschitz condition. We give a probabilistic interpretation of the solution in Sobolev spaces using reflected forward–backward stochastic differential equations, doubly reflected forward–backward stochastic differential equations and the penalization method.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493708002305

Reference11 articles.

1. G. Barles and E. Lesign, SDE, BSDE and PDE, Pitman Research Notes in Maths. Series 364 (Longman, 1997) pp. 47–80.

2. Lecture Notes in Math.;Bouleau N.,1989

3. Viscosity solutions of Hamilton-Jacobi equations

4. User’s guide to viscosity solutions of second order partial differential equations

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