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On a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition
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B. Boufoussi
Published/Copyright:
December 1, 2006
We consider the following generalized BSDE:
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 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.
Published Online: 2006-12-01
Published in Print: 2006-12-01
Copyright 2006, Walter de Gruyter
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