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Probabilistic representation of solutions for quasi-linear parabolic PDE via FBSDE with reflecting boundary conditions

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Abstract

A probabilistic representation of the solution (in the viscosity sense) of a quasi-linear parabolic PDE system with non-lipschitz terms and a Neumann boundary condition is given via a fully coupled forward-backward stochastic differential equation with a reflecting term in the forward equation. The extension of previous results consists on the relaxation on the Lipschitz assumption on the drift coefficient of the forward equation, using a previous result of the authors.

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain

    Pedro Marín-Rubio & José Real

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  1. Pedro Marín-Rubio
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  2. José Real
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Correspondence to Pedro Marín-Rubio.

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Marín-Rubio, P., Real, J. Probabilistic representation of solutions for quasi-linear parabolic PDE via FBSDE with reflecting boundary conditions. SeMA 51, 109–116 (2010). https://doi.org/10.1007/BF03322561

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  • DOI: https://doi.org/10.1007/BF03322561

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