Integral representation with respect to fractional Brownian motion under a log-Hölder assumption

Taras Shalaiko; Georgiy Shevchenko

doi:10.15559/15-vmsta35cnf

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arXiv · 1509.03894

Integral representation with respect to fractional Brownian motion under a log-Hölder assumption

Taras Shalaiko·Georgiy Shevchenko

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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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Taras Shalaiko, Georgiy Shevchenko. 2015-10-07. Integral representation with respect to fractional Brownian motion under a log-Hölder assumption. https://doi.org/10.15559/15-vmsta35cnf

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