Non-linear Gaussian smoothing with Taylor moment expansion

TL;DR

This paper introduces a Gaussian smoothing method using Taylor moment expansion (TME) to approximate transition densities in stochastic differential equations, providing theoretical error bounds and demonstrating practical effectiveness through numerical experiments.

Contribution

The paper proposes a novel TME-based Gaussian smoothing approach with stability analysis and error bounds, advancing continuous-discrete smoothing techniques.

Findings

The TME smoothing method is stable under weak assumptions.

Theoretical error bounds are derived for the TME estimates.

Numerical experiments confirm practical effectiveness.

Abstract

This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the stochastic differential equation in the dynamic model. Furthermore, we derive a theoretical error bound (in the mean square sense) of the TME smoothing estimates showing that the smoother is stable under weak assumptions. Numerical experiments are presented in order to illustrate practical use of the method.