Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations.
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Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process
Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We study a free energy computation procedure, introduced in [Darve and Pohorille, J. Chem. Phys.115 (2001) 9169–9183; Hénin and Chipot, J. Chem. Phys.121 (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre et al., Nonlinearity21 (2008) 1155–1181],...
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