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Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs


Authors: Adrien Laurent and Gilles Vilmart
Journal: Math. Comp. 89 (2020), 169-202
MSC (2010): Primary 60H35, 37M25, 65L06, 41A58
DOI: https://doi.org/10.1090/mcom/3455
Published electronically: June 24, 2019
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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.


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Additional Information

Adrien Laurent
Affiliation: Ecole Normale Supérieure de Rennes and Université de Rennes 1, Campus de Ker Lann, avenue Robert Schumann, F-35170 Bruz, France
Address at time of publication: Université de Genève, Section de mathématiques, 2-4 rue du Lièvre, CP 64, CH-1211 Genève 4, Switzerland
Email: Adrien.Laurent@unige.ch

Gilles Vilmart
Affiliation: Université de Genève, Section de mathématiques, 2-4 rue du Lièvre, CP 64, CH-1211 Genève 4, Switzerland
Email: Gilles.Vilmart@unige.ch

DOI: https://doi.org/10.1090/mcom/3455
Keywords: Stochastic differential equations, invariant measure, ergodicity, exotic aromatic trees, order conditions
Received by editor(s): May 1, 2018
Received by editor(s) in revised form: January 30, 2019
Published electronically: June 24, 2019
Additional Notes: This work was partially supported by the Swiss National Science Foundation, grants No. 200021_162404, 200020_178752 and 200020_144313/1
Article copyright: © Copyright 2019 American Mathematical Society