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The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6


 
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1. Title Title of document The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6
 
2. Creator Author's name, affiliation, country Ivan Nourdin; Université Nancy 1; France
 
2. Creator Author's name, affiliation, country Anthony Réveillac; Humboldt-University; Germany
 
2. Creator Author's name, affiliation, country Jason Swanson; University of Central Florida; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic integration; Stratonovich integral; fractional Brownian motion; weak convergence; Malliavin calculus
 
3. Subject Subject classification 60H05; 60G15; 60G18; 60J05.
 
4. Description Abstract Let $B$ be a fractional Brownian motion with Hurst parameter $H=1/6$. It is known that the symmetric Stratonovich-style Riemann sums for $\int\!g(B(s))\,dB(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian motion that is independent of $B$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR; DFG; NSA
 
7. Date (YYYY-MM-DD) 2010-12-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/843
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-843
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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