A second order time discretization of the solution of the non-linear filtering problem

TL;DR

This paper introduces a second-order time discretization method for the non-linear filtering problem, achieving a convergence rate proportional to the square of the partition mesh, improving numerical approximation accuracy.

Contribution

The paper presents a novel second-order discretization scheme for non-linear filtering, enhancing the precision of numerical solutions for continuous-time filtering problems.

Findings

Convergence rate is proportional to the square of the mesh size.

The discretization method improves approximation accuracy.

Applicable to functionals parametrized by observation paths.

Abstract

The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of these functionals corresponding to a chosen partition of the time interval and show that the convergence rate of discretisation is proportional with the square of the mesh of the partition.