Weak backward error analysis for SDEs. (English) Zbl 1256.65002
This paper shows that for the Euler-Maruyama method applied to a stochastic differential equation (SDE), it possesses a modified Kolmogorov operator that can be expanded in powers of the stepsize. In the case the SDE is elliptic or hypoelliptic, a weak backward error analysis result holds. This implies that every invariant measure of the method is close to a modified invariant measure obtained by asymptotic expansion, and that the method is exponentially mixing up to some very small error and for all times.
Reviewer: Kevin Burrage (Brisbane)
MSC:
65C30 | Numerical solutions to stochastic differential and integral equations |
60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
65L70 | Error bounds for numerical methods for ordinary differential equations |
34F05 | Ordinary differential equations and systems with randomness |