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When does fractional Brownian motion not behave as a continuous function with bounded variation?

If we compose a smooth function g with fractional Brownian motion B with Hurst index , then the resulting change of variables formula (or Itô formula) has the same form as if fractional Brownian motion was a continuous function with bounded variation. In this note we prove a new integral representation formula for the running maximum of a continuous function with bounded variation. Moreover we show that the analogy to fractional Brownian motion fails.
Year of publication:
2010
Authors: Azmoodeh, Ehsan ; Tikanmäki, Heikki ; Valkeila, Esko
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 80.2010, 19-20, p. 1543-1550
Publisher: Elsevier
Keywords: Function of bounded variation Fractional Brownian motion Pathwise stochastic integral Running maximum process
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10008868939
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