We prove existence and uniqueness for two classes of martingale problems
involving a nonlinear but bounded drift coefficient. In the first class,
this coefficient depends on the time , the position and the marginal
of the solution at time . In the second, it depends on , and ,
the density of the time marginal w.r.t. Lebesgue measure. As far as the
dependence on and is concerned, no continuity assumption is made.
The results, first proved for the identity diffusion matrix, are extended...
We study a free energy computation procedure, introduced in
[Darve and Pohorille,
(2001) 9169–9183; Hénin and Chipot,
(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 ,
(2008) 1155–1181],...
The Diffusion Monte Carlo method is devoted to the computation of
electronic ground-state energies of molecules. In this paper, we focus on
implementations of this method which consist in exploring the
configuration space with a fixed number of random walkers evolving
according to a stochastic differential equation discretized in time. We
allow stochastic reconfigurations of the walkers to reduce the
discrepancy between the weights that they carry. On a simple
one-dimensional example, we prove...
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