Journal article
Stochastic analysis, rough path analysis and fractional Brownian motions
- Abstract:
- In this paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we furthermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordingly. The method can actually be applied to a larger class of Gaussian processes with covariance functions satisfying a simple decay condition.
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- Publisher copy:
- 10.1007/s004400100158
Authors
- Journal:
- Probability Theory and Related Fields More from this journal
- Volume:
- 122
- Issue:
- 1
- Pages:
- 108-140
- Publication date:
- 2002-01-01
- DOI:
- EISSN:
-
1432-2064
- ISSN:
-
0178-8051
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:2828
- UUID:
-
uuid:5dbae643-ad46-482f-8530-a4059e2ef3c3
- Local pid:
-
pubs:2828
- Source identifiers:
-
2828
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright date:
- 2002
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