Integral representation with respect to fractional Brownian motion under a log-Hölder assumption
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 219–232
Pub. online: 25 September 2015
Type: Research Article
Open Access
Open Access
Received
6 September 2015
6 September 2015
Revised
13 September 2015
13 September 2015
Accepted
14 September 2015
14 September 2015
Published
25 September 2015
25 September 2015
Abstract
We show that if a random variable is the final value of an adapted log-Hölder 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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