Exotic aromatic B-series for the study of long time integrators
for a class of ergodic SDEs
A. Laurent and G. Vilmart
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.
Key Words. stochastic differential equations, invariant measure, ergodicity, exotic aromatic trees, order conditions.