Analysis of a micro–macro acceleration method with minimum relative entropy moment matching

Tony Lelièvre, Giovanni Samaey and Przemysław Zieliński

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3753-3801

Abstract: We analyse convergence of a micro–macro acceleration method for the simulation of stochastic differential equations with time-scale separation. The method alternates short bursts of path simulations with the extrapolation of macroscopic state variables forward in time. After extrapolation, a new microscopic state is constructed, consistent with the extrapolated macroscopic state, that minimises the perturbation caused by the extrapolation in a relative entropy sense. We study local errors and numerical stability of the method to prove its convergence to the full microscopic dynamics when the extrapolation time step tends to zero and the number of macroscopic state variables tends to infinity.

Keywords: Micro–macro simulations; Entropy optimisation; Stiff stochastic differential equations; Kullback–Leibler divergence; Weak convergence (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:6:p:3753-3801

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DOI: 10.1016/j.spa.2019.10.008

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