Dr. Jost Pieper (University of Durham) – An application of rough SDEs to robust filtering with jumps

Finding a robust representation of the conditional distribution of a signal given a noisy observation is a classical problem in stochastic filtering. Such representations are of interest as they justify the use of discrete observation data and ensure robustness of the signal approximation to slight model misspecification.

When the signal and observation are correlated through their noise, Crisan, Diehl, Friz, and Oberhauser (2013) showed that such a robust representation typically cannot exist as a functional on the space of continuous paths, but must instead be formulated on the space of geometric rough paths.

In this talk, I will discuss how to extend these results to stochastic filtering problems involving correlated multidimensional jump diffusions, using the theory of rough stochastic differential equations (RSDEs) with jumps. Specifically, I will discuss the consistency of (randomised) RSDEs with their purely stochastic counterparts, as well as exponential moment bounds provided by a version of the John–Nirenberg inequality for BMO processes with jumps, as first introduced by Lê in 2022.

Building on these results, I will then address the existence of a robust representation of the conditional distribution in a filtering model with correlation in both the continuous and jump noise.

This is an ongoing work with Andrew Allan and Josef Teichmann.