Particle Filters for Multiscale Diffusions

TL;DR

This paper introduces a particle filter tailored for multiscale stochastic systems, leveraging their structure to improve the efficiency of approximating the optimal filter in partially observed, slow-scale systems.

Contribution

It presents a novel particle filtering method that exploits multiscale properties to enhance computational efficiency in filtering tasks.

Findings

Efficient approximation of the optimal filter in multiscale systems.

Demonstrated advantages over traditional filters in computational speed.

Applicable to systems with partial observations at slow time scales.

Abstract

We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the optimal filter.