When does fractional Brownian motion not behave as a continuous function with bounded variation?
Ehsan Azmoodeh,
Heikki Tikanmäki and
Esko Valkeila
Statistics & Probability Letters, 2010, vol. 80, issue 19-20, 1543-1550
Abstract:
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.
Keywords: Function; of; bounded; variation; Fractional; Brownian; motion; Pathwise; stochastic; integral; Running; maximum; process (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00169-0
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:80:y:2010:i:19-20:p:1543-1550
Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01
Access Statistics for this article
Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul
More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().