Long time accuracy of Lie-Trotter splitting methods
for Langevin dynamics
A. Abdulle, G. Vilmart, and K.C. Zygalakis
Abstract. A new characterization of sufficient conditions for the Lie-Trotter splitting to capture the numerical invariant measure of nonlinear ergodic Langevin dynamics up to
an arbitrary order is discussed. Our characterization relies on backward error analysis
and needs weaker assumptions than assumed so far in the literature. In particular,
neither high weak order of the splitting scheme nor symplecticity are necessary to
achieve high order approximation of the invariant measure of the Langevin dynamics.
Numerical experiments confirm our theoretical findings.
Key Words. stochastic differential equations, splitting method, Langevin dynamics, weak convergence, modified differential
equations, backward error analysis, invariant measure, ergodicity.