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Strong solutions of d-dimensional SDE's with generalized drift and fractional Brownian initial noise

Ortiz-Latorre, Salvador; Pilipenko, Andrey; Proske, Frank Norbert; Baños, David Ruiz
Journal article; SubmittedVersion
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1705.01616.pdf (369.9Kb)
Year
2017
Permanent link
http://urn.nb.no/URN:NBN:no-58157

CRIStin
1468381

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Appears in the following Collection
  • Matematisk institutt [2422]
  • CRIStin høstingsarkiv [15189]
Original version
arXiv.org. 2017
Abstract
In this paper we prove the existence of strong solutions to a SDE with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<1/2. Here the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a "local time variational calculus" argument.
 
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