Long time numerical solution of stochastic differential equations

Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern
Philosophischnaturwissenschaftliche Fakultät
Departement Mathematik und Statistik
Mathematisches Institut
Mathematical Colloquia
____________________________________________________________________________
Monday, 07 November2016
17:15 h, Lecture Room B 78
Dr. Gilles Vilmart, University of Geneva
Long time numerical solution of stochastic
differential equations: the interplay of geometric
integration and stochastic integration
Abstract:
Numerous physical (or chemical) phenomena can be modeled by differential equations
which possess a particular geometric structure. There are situations where preserving numerically such a structure reveals essential for an accurate integration, and this is the aim
of the theory of geometric numerical integration. For example, a good energy conservation
by the numerical integrator is crucial for an accurate long time solution of an n-body problem in molecular dynamics or in astronomy for the evolution of the solar system simulated
over millions of years.
In this talk we highlight the role that some geometric integration tools that were originally
introduced in the deterministic setting play in the design of new accurate integrators to
sample the invariant distribution of ergodic systems of stochastic ordinary and partial
differential equations.
This talk is based on joint works with Assyr Abdulle (EPF Lausanne), Charles-Edouard
Bréhier (Univ. Lyon) and Konstantinos C. Zygalakis (Univ. Edinburgh).
Sekretariat, Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern, Tel. +41 (0)31 631 88 21, Fax +41 (0)31 631 85 10
[email protected], www.math.unibe.ch

Download Report