872 research outputs found
A symmetry-adapted numerical scheme for SDEs
We propose a geometric numerical analysis of SDEs admitting Lie symmetries
which allows us to individuate a symmetry adapted coordinates system where the
given SDE has notable invariant properties. An approximation scheme preserving
the symmetry properties of the equation is introduced. Our algorithmic
procedure is applied to the family of general linear SDEs for which two
theoretical estimates of the numerical forward error are established.Comment: A numerical example adde
Integration by parts formulas and Lie's symmetries of SDEs
A strong quasi-invariance principle and a finite-dimensional integration by
parts formula as in the Bismut approach to Malliavin calculus are obtained
through a suitable application of Lie's symmetry theory to autonomous
stochastic differential equations. The main stochastic, geometrical and
analytical aspects of the theory are discussed and applications to some
Brownian motion driven stochastic models are provided
Strong Kac's chaos in the mean-field Bose-Einstein Condensation
A stochastic approach to the (generic) mean-field limit in Bose-Einstein
Condensation is described and the convergence of the ground state energy as
well as of its components are established. For the one-particle process on the
path space a total variation convergence result is proved. A strong form of
Kac's chaos on path-space for the -particles probability measures are
derived from the previous energy convergence by purely probabilistic techniques
notably using a simple chain-rule of the relative entropy. The Fisher's
information chaos of the fixed-time marginal probability density under the
generic mean-field scaling limit and the related entropy chaos result are also
deduced
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