Convergence of the likelihood ratio method for linear response of non-equilibrium stationary states
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2021
- Source ID
- 10.1051/m2an/2020050
Entities
People
- Gabriel Stoltz
- Petr Plecháč
- Ting Wang
Organizations
- Agence Nationale de la Recherche
- Defense Advanced Research Projects Agency
- United States Army Research Laboratory