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- Title
On a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition.
- Authors
Boufoussi, B.; Mrhardy, N.
- Abstract
We consider the following generalized BSDE: (i) Yt = ξ + ∫Tt f(s, w, Ys, Zs)ds + ∫Tt h(s, w, Ys)dks - ∫Tt ZsdBs + ∫R(LxT(Y) - Lxt(Y))ν(dx), ∀ 0 ≤ t ≤ T, (ii) E (sup0≤t≤T |Yt|2 + ∫T0 &VerbarZt2dt) < ∞. where(Bt, 0 ≤ t ≤ T) is a d-dimensional Brownian motion, ξ is the terminal value, {kt, 0 ≤ t ≤ T} is a continuous real valued increasing process such that k0 = 0, ν is a signed measure onR and Lxt(Y) is the symmetric local time of the semimartingale Y. Under some continuous and linear growth conditions on the coefficients f and h, we will prove existence result for equation of the type (1). As a consequence we will give a probabilistic representation to the solution of a nonlinear partial differential equations with Neumann boundary conditions.
- Subjects
PARTIAL differential equations; NONLINEAR differential equations; NONLINEAR partial differential operators; NONLINEAR boundary value problems; SEMIMARTINGALES (Mathematics); NEUMANN problem
- Publication
Random Operators & Stochastic Equations, 2006, Vol 14, Issue 4, p367
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/156939706779801723