Rough SDEs and Robust Filtering for Jump-Diffusions

TL;DR

This paper develops a robust filtering framework for multidimensional jump-diffusions using rough path theory, establishing new stability results for stochastic filters in complex jump-diffusion models.

Contribution

It introduces a novel rough stochastic differential equation approach for robust filtering in jump-diffusions, extending the theory to include jumps and rough path analysis.

Findings

Established existence of continuous conditional distribution representations.

Proved robustness of stochastic filters via rough path analysis.

Analyzed exponential moments and Skorokhod continuity for jump-diffusions.

Abstract

We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in general such a representation can only be continuous with respect to rough path topologies, leading us naturally to express the conditional dynamics as a rough stochastic differential equation with jumps. Via the analysis of such equations, including exponential moments, Skorokhod continuity, and randomisation of the rough path, we establish several novel robustness results for stochastic filters.