caa a22 4500 605497087 CHVBK 20210128105157.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10543-015-0546-0 doi (NATIONALLICENCE)springer-10.1007/s10543-015-0546-0 Kopec Marie ENS RENNES/INRIA RENNES, Campus de Ker Lann, Avenue Robert Schumann, 35170, Bruz, France aut Weak backward error analysis for Langevin process [Elektronische Daten] [Marie Kopec] We consider numerical approximations of stochastic Langevin equations by implicit methods. 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. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamics associated with the considered implicit scheme is exponentially mixing: The law of the scheme converges exponentially fast to a constant up to an error that we can optimize. Springer Science+Business Media Dordrecht, 2015 Backward error analysis nationallicence Langevin equation nationallicence Exponential mixing nationallicence Numerical scheme nationallicence Weak error nationallicence Kolmogorov equation nationallicence BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1057-1103 0006-3835 55:4<1057 2015 55 10543 https://doi.org/10.1007/s10543-015-0546-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-015-0546-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kopec Marie ENS RENNES/INRIA RENNES, Campus de Ker Lann, Avenue Robert Schumann, 35170, Bruz, France aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/4(2015-12-01), 1057-1103 0006-3835 55:4<1057 2015 55 10543 SWISSBIB 394790812