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The FBM Itô's Formula Through Analytic Continuation


 
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1. Title Title of document The FBM Itô's Formula Through Analytic Continuation
 
2. Creator Author's name, affiliation, country D. Feyel; Université de Evry
 
2. Creator Author's name, affiliation, country A. de La Pradelle; Université Paris VI
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Wiener space, Sobolev space, Stochastic integral, FractionalBrownian Motion, Itô's formula.
 
3. Subject Subject classification 60H05, 60H07
 
4. Description Abstract The Fractional Brownian Motion can be extended to complex values of the parameter $\alpha $ for $\Re\alpha >{1\over 2}$. This is a useful tool. Indeed, the obtained process depends holomorphically on the parameter, so that many formulas, as Itô formula, can be extended by analytic continuation. For large values of $\Re\alpha $, the stochastic calculus reduces to a deterministic one, so that formulas are very easy to prove. Hence they hold by analytic continuation for $\Re\alpha \le 1$, containing the classical case $\alpha =1$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2001-10-01
 
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/99
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-99
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en
 
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