Symmetrized importance samplers for stochastic differential equations

TL;DR

This paper introduces symmetrized importance sampling methods for stochastic differential equations, showing that simple symmetrization can substantially enhance performance, especially in small-noise regimes, with promising applications like data assimilation.

Contribution

The paper proposes a novel symmetrization technique for importance sampling in SDEs, improving efficiency over existing methods in small-noise scenarios.

Findings

Symmetrization improves importance sampling performance.

Effective in linear and nonlinear SDE examples.

Potential for applications like data assimilation.

Abstract

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed.