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Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions


 
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1. Title Title of document Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions
 
2. Creator Author's name, affiliation, country Fabrice Baudoin; Purdue University; United States
 
2. Creator Author's name, affiliation, country Xuejing Zhang; Purdue University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) taylor expansion, fractional Brownian motion
 
4. Description Abstract We study the Taylor expansion for the solution of a differential equation driven by a multi-dimensional Hölder path with exponent  $H> 1/2$. We derive a convergence criterion that enables us to write the solution as an infinite sum of iterated integrals on a non empty interval. We apply our deterministic results to stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H > 1/2$. We also study the convergence in L2 of the stochastic Taylor expansion by using L2 estimates of iterated integrals and Borel-Cantelli type arguments.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-07-06
 
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/2136
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2136
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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