A Levy-area between Brownian motion and rough paths with applications to robust non-linear filtering and RPDEs

Abstract

We give meaning to differential equations with a rough path term and a Brownian noise term as driving signals. Such differential equations as well as the question of regularity of the solution map arise naturally and we discuss two applications: one revisits Clark's robustness problem in nonlinear filtering, the other is a Feynman--Kac type representation of linear RPDEs. En passant, we give a short and direct argument that implies integrability estimates for rough differential equations with Gaussian driving signals which is of independent interest.

New coauthor, new section on integrability for Gaussian RDEs, minor changes

References in corpus (1)

• Non-standard approximations of the Ito-map

Cited by in corpus (6)

• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• Robust filtering: Correlated noise and multidimensional observation
• Rough nonlocal diffusions
• Pathwise Itô Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients
• Transportation-cost inequalities for diffusions driven by Gaussian processes
• Approximate Likelihood Construction for Rough Differential Equations