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Stochastic parameterizations of deterministic dynamical systems: Theory, applications and challenges
mardi 31 jan 2017
Workshop on Multiscale methods for stochastic dynamics 1Stochastic parameterizations of deterministic dynamical systems: Theory,...
43:262Ergodic Stochastic Differential Equations and Sampling: A numerical analysis...
44:283Weak convergence for semi-linear SPDEs.
43:094On stochastic numerical methods for the approximative pricing of financial...
41:175Mean-square stability analysis of SPDE approximations.
38:526Adaptive timestepping for S(P)DEs to control growth.
44:437Noise-induced transitions and mean field limits for multiscale diffusions.
44:208Accelerated dynamics and transition state theory.
45:599Long-time homogenization of the wave equation.
Stochastic parameterizations of deterministic dynamical systems: Theory, applications and challenges.
There is an increased interest in the stochastic parameterization of deterministic dynamical systems whereby a high-dimensional deterministic dynamical system is reduced to a low-dimensional stochastically driven system.
We discuss standard techniques of stochastic model reduction such as homogenization. Recently rigorous results have been obtained justifying this method. The theory relies on an asymptotic limit of infinite time scale separation which is not always satisfied in real world applications. We present a new method to go beyond this asymptotic limit by employing Edgeworth approximations.
This is joint work with Jeroen Wouters.