Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise
Probability
2018-04-11 v2
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.
Keywords
Cite
@article{arxiv.1705.01616,
title = {Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise},
author = {David R. Baños and Salvador Ortiz-Latorre and Andrey Pilipenko and Frank Proske},
journal= {arXiv preprint arXiv:1705.01616},
year = {2018}
}
Comments
45 pages. arXiv admin note: text overlap with arXiv:1511.02717