mercredi 01 fév 2017
Workshop on Multiscale methods for stochastic dynamics
1Stochastic parameterizations of deterministic dynamical systems: Theory,...
2Ergodic Stochastic Differential Equations and Sampling: A numerical analysis...
3Weak convergence for semi-linear SPDEs.
4On stochastic numerical methods for the approximative pricing of financial...
5Mean-square stability analysis of SPDE approximations.
6Adaptive timestepping for S(P)DEs to control growth.
7Noise-induced transitions and mean field limits for multiscale diffusions.
8Accelerated dynamics and transition state theory.
9Long-time homogenization of the wave equation.

43:26

44:28

43:09

41:17

38:52

44:43

44:20

45:59

42:13
We introduce a class of adaptive timestepping strategies for stochastic differential equations such as those arising from the semi-discretization of SPDEs with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme. We prove that the Euler-Maruyama scheme with an adaptive timestepping strategy in this class is strongly convergent and present preliminary results on a semi-implicit scheme and an extension to non-Lipschitz noise terms. We test this alternative to taming on some examples. This is joint work with Conall Kelly.