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Mathematics > Probability

arXiv:1301.3799 (math)
[Submitted on 16 Jan 2013 (v1), last revised 2 Jan 2014 (this version, v2)]

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

Authors: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.
Comments: New coauthor, new section on integrability for Gaussian RDEs, minor changes
Subjects: Probability (math.PR)
Cite as: arXiv:1301.3799 [math.PR]
  (or arXiv:1301.3799v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1301.3799

Submission history

From: Harald Oberhauser [view email]
[v1] Wed, 16 Jan 2013 19:47:20 UTC (17 KB)
[v2] Thu, 2 Jan 2014 10:30:18 UTC (21 KB)
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