Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics

Nicolas Perrin 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, finding an efficient method to simulate the numerical solution of PB equation is very useful. In this paper, we establish a probabilistic interpretation of the nonlinear PB equation with Backward Stochastic Differential Equations (BSDEs). This interpretation requires an adaptation of existing results on BSDEs.
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Nicolas Perrin. Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics. 2012. ⟨hal-00648180v3⟩

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