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

Tags

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.