Ergodic Stochastic Differential Equations and Sampling: A numerical analysis perspective
mardi 31 jan 2017
Workshop on Multiscale methods for stochastic dynamics
1Stochastic parameterizations of deterministic dynamical systems: Theory,...
43:26
2Ergodic Stochastic Differential Equations and Sampling: A numerical analysis...44:28
3Weak convergence for semi-linear SPDEs.43:09
4On stochastic numerical methods for the approximative pricing of financial...41:17
5Mean-square stability analysis of SPDE approximations.38:52
6Adaptive timestepping for S(P)DEs to control growth.44:43
7Noise-induced transitions and mean field limits for multiscale diffusions.44:20
8Accelerated dynamics and transition state theory.45:59
9Long-time homogenization of the wave equation.42:13
Ergodic Stochastic Differential Equations and Sampling: A numerical analysis perspective.
Understanding the long time behaviour of solutions to ergodic stochastic differential equations is an important question with relevance in many field of applied mathematics and statistics. Hence, designing appropriate numerical algorithms that are able to capture such behaviour correctly is extremely important. A recently introduced framework [1,2,3] using backward error analysis allows us to characterise the bias with which one approximates the invariant measure (in the absence of the accept/reject correction). These ideas will be used to design numerical methods exploiting the variance reduction of recently introduced nonreversible Langevin samplers [4]. Finally if there is time we will discuss, how things ideas can be combined with the idea of Multilevel Monte Carlo [5] to produce unbiased estimates of ergodic averages without the need the of an accept-reject correction [6] and optimal computational cost.