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Near Boltzmann-Gibbs measure preserving stochastic variational integrator

Friday 28th March 2008 - 10:05 to 10:35
INI Seminar Room 1

This talk presents an explicit, structure-preserving probablistic numerical integrator for Langevin systems, and an efficient, structure-preserving integrator for Langevin systems with holonomic constraints. In a nut-shell, the method does for the Boltzmann-Gibbs measure what symplectic integrators do for energy. More precisely, we prove the method very nearly preserves the Boltzmann-Gibbs measure. As a consequence of its variational design, the algorithm also exactly preserves the symplectic area change associated to Langevin processes. The method with supporting theory enables one to take time-step sizes and friction factors at the limit of stability of the integration scheme (e.g., the time-step size must be smaller than the fastest characteristic frequency in the system).

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons