Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Likelihood Ratio Methods for Sensitivity Analysis and Linear Response Estimation of Non-equilibrium Stationary States
Petr Plechac (University of Delaware)
Abstract:
In many applications one is interested in estimating the response of the steady-state distribution of a stochastic dynamical system under a perturbation to the dynamics.
For example, such computations form a basis for using the linear response theory of statistical mechanics in estimating transport coefficients that relate the average response of the system at its steady state to the external forcing applied to the system, e.g., the mobility, the shear viscosity and the thermal conductivity.
We briefly review a background of linear response theory and then we discuss new schemes based on Girsanov's change-of-measure theory for computing the sensitivity or linear response of steady-state averages of stochastic dynamics.
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.
We discuss numerical analysis of such schemes by presenting 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 needed for steady-state sampling.
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.
(joint work with T. Wang and G. Stoltz).
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