Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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Page(s) | S593 - S623 | |
DOI | https://doi.org/10.1051/m2an/2020050 | |
Published online | 26 February 2021 |
Convergence of the likelihood ratio method for linear response of non-equilibrium stationary states
1
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
2
Université Paris-Est, CERMICS, ENPC, INRIA, Paris, France
3
Physical Modeling & Simulation Branch, CISD, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
* Corresponding author: tingw@udel.edu
Received:
7
February
2020
Accepted:
23
July
2020
We consider numerical schemes for computing the linear response of steady-state averages with respect to a perturbation of the drift part of the stochastic differential equation. The schemes are based on the Girsanov change-of-measure theory in order to reweight trajectories with factors derived from a linearization of the Girsanov weights. The resulting estimator is the product of a time average and a martingale correlated to this time average. We investigate both its discretization and finite-time approximation errors. The designed numerical schemes are shown to be of a bounded variance with respect to the integration time which is desirable feature for long time simulations. We also show how the discretization error can be improved to second-order accuracy in the time step by modifying the weight process in an appropriate way.
Mathematics Subject Classification: 65C05 / 65C20 / 65C40 / 60J27 / 60J75
Key words: Non-equilibrium steady states / linear response / stochastic differential equations / likelihood ratio method / variance reduction
© EDP Sciences, SMAI 2021
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