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B. Boufoussi, N. Mrhardy

On a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition

We consider the following generalized BSDE:

where (B_t , 0 ? t ? T) is a d-dimensional Brownian motion, ξ is the terminal value, {k_t , 0 ? t ? T} is a continuous real valued increasing process such that k ₀ = 0, ? is a signed measure on and is the symmetric local time of the semimartingale Y.

Under some continuous and linear growth conditions on the coefficients ƒ 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.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 14, 12/2006
Pages: 367 - 384

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