Arnaud Debussche
Weak backward error analysis for SDEs.
Wed, 05/04/2011 - 15:01 — SomNambulAuthors: Erwan Faou, Arnaud Debussche
Subjects: Numerical Analysis
AbstractWe consider numerical approximations of stochastic differential equations by
the Euler method. In the case where the SDE is elliptic or hypoelliptic, we
show a weak backward error analysis result in the sense that the generator
associated with the numerical solution coincides with the solution of a
modified Kolmogorov equation up to high order terms with respect to the
stepsize.Asymptotic behavior of stochastic PDEs with random coefficients.
Thu, 03/04/2010 - 16:01 — SomNambulAuthors: Arnaud Debussche, Da Prato Giuseppe
Subjects: Analysis of PDEs
AbstractWe study the long time behavior of the solution of a stochastic PDEs with
random coefficients assuming that randomness arises in a different independent
scale. We apply the obtained results to 2D- Navier--Stokes equations.Scalar conservation laws with stochastic forcing.
Mon, 02/01/2010 - 16:01 — SomNambulAuthors: Arnaud Debussche, Julien Vovelle
Subjects: Analysis of PDEs
AbstractWe show that the Cauchy Problem for a randomly forced, periodic
multi-dimensional scalar first-order conservation law with additive or
multiplicative noise is well-posed: it admits a unique solution, characterized
by a kinetic formulation of the problem, which is the limit of the solution of
the stochastic parabolic approximation.Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Arnaud Debussche, Ludovic Goudenège
Subjects: Analysis of PDEs
AbstractWe consider a stochastic partial differential equation with two logarithmic
nonlinearities, with two reflections at 1 and -1 and with a constraint of
conservation of the space average. The equation, driven by the derivative in
space of a space-time white noise, contains a bi-Laplacian in the drift.
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