Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs

Abstract

We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the invariant measure of a class of ergodic stochastic differential equations (SDEs) with additive noise. The proposed analysis covers Runge-Kutta type schemes including the cases of partitioned methods and postprocessed methods. We also show that the introduced exotic aromatic B-series satisfy an isometric equivariance property.

33 pages

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• Variance Reduction using Nonreversible Langevin Samplers
• High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise
• Formal series and numerical integrators: some history and some new techniques

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• The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators
• Approximations of dispersive PDEs in the presence of low-regularity randomness
• A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics
• Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
• Higher Order Generalization Error for First Order Discretization of Langevin Diffusion