Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527319 | Stochastic Processes and their Applications | 2015 | 26 Pages |
Abstract
We study the existence and uniqueness of the solution for the following backward stochastic variational inequality with oblique reflection (for short, BSVI(H(t,y)âÏ(y))), written under differential form {âdYt+H(t,Yt)âÏ(Yt)(dt)âF(t,Yt,Zt)dtâZtdBt,tâ[0,T],YT=η, where H is a bounded symmetric smooth matrix and Ï is a proper convex lower semicontinuous function, with âÏ being its subdifferential operator. The presence of the product HâÏ does not permit the use of standard techniques because it conserves neither the Lipschitz property of the matrix nor the monotonicity property of the subdifferential operator. We prove that, if we consider the dependence of H only on the time, the equation admits a unique strong solution and, allowing the dependence on the state of the system, the above BSVI(H(t,y)âÏ(y)) admits a weak solution in the sense of the Meyer-Zheng topology. However, for that purpose we must renounce at the dependence on Z for the generator function and we situate our problem in a Markovian framework.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Anouar M. Gassous, Aurel RÄÅcanu, Eduard Rotenstein,