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arXiv · 1301.3799

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

Joscha Diehl·Harald Oberhauser·Sebastian Riedel
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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.

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Joscha Diehl, Harald Oberhauser, Sebastian Riedel. 2014-01-02. A Levy-area between Brownian motion and rough paths with applications to robust non-linear filtering and RPDEs. https://arxiv.org/abs/1301.3799

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