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Integral representation with respect to fractional Brownian motion under a log-Hölder assumption (1509.03894v2)
Published 13 Sep 2015 in math.PR
Abstract: We show that if a random variable is the final value of an adapted log-H\"{o}lder continuous process, then it can be represented as a stochastic integral with respect to a fractional Brownian motion with adapted integrand. In order to establish this representation result, we extend the definition of the fractional integral.
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