Volume 55, 2021Regular 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
|Page(s)||S593 - S623|
|Published online||26 February 2021|
Convergence of the likelihood ratio method for linear response of non-equilibrium stationary states
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: firstname.lastname@example.org
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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