### Weak backward error analysis for stochastic differential equations

Faou, E *(IRISA/INRIA)*

Wednesday 30 June 2010, 14:10-15.00

Seminar Room 1, Newton Institute

#### Abstract

Backward error analysis is a powerful tool to understand the long time behavior of discrete approximations of deterministic differential equations. Roughly speaking, it can be shown that a discrete numerical solution associated with an ODE can be interpreted as the exact solution of a modified ODE over extremely long time with respect to the time discretization parameter.
In this work, we consider numerical simulations of SDEs and we show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. In the case where the SDE possesses a unique invariant measure with exponentially mixing properties, this implies that the numerical solution remains exponentially mixing for a modified quasi invariant measure over very long time. This is a joint work with Arnaud Debussche (ENS Cachan Bretagne).

#### Video

**The video for this talk should appear here if JavaScript is enabled.**

If it doesn't, something may have gone wrong with our embedded player.

We'll get it fixed as soon as possible.

## Comments

Start the discussion!