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Weak backward error analysis for stochastic differential equations

Presented by: 
E Faou [IRISA/INRIA]
Date: 
Wednesday 30th June 2010 - 14:10 to 15:00
Venue: 
INI Seminar Room 1
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).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons