Fellow members of Mathematics Department,

Our first CAM seminar of the semester will be an online one and it will
take place tomorrow,

October 6, 2021 3:35 - 4:35pm

via Zoom
https://tennessee.zoom.us/j/99892953493

The speaker will be 

Petr Plechac (University of Delaware)

The title and abstract are below.

See you all there tomorrow,
Abner

===================
Title: Likelihood ratio methods for estimating linear response of non-
equilibrium steady states.

Absract:
In statistical mechanics, linear response is the measure to quantify
the average response of a steady state to the small external
perturbation of stochastic system. In this talk, we discuss numerical
schemes for the linear response  computations of invariant measures
from fluctuations at equilibrium. The schemes are based on Girsanov's
change-of-measure theory  and apply reweighting of trajectories by
factors derived from a linearization of the Girsanov weights. This
approach leads to a class of estimators we call  martingale product
estimators.

We investigate both the discretization error and  the finite time
approximation error. The designed numerical schemes are shown to be of
bounded variance with respect to the integration time, which is a
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. 
The resulted methodology provides an alternative  computational
approach to classical linear response methods such as the Green-Kubo
approach. We provide some numerical evidences to demonstrate the
efficiency and accuracy of the method.


(joint work with Gabriel Stoltz and Ting Wang)





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