Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion

Andreas Neuenkirch () and Ivan Nourdin ()
Additional contact information
Andreas Neuenkirch: Johann Wolfgang Goethe-Universität Frankfurt
Ivan Nourdin: Université Pierre et Marie Curie Paris 6

Journal of Theoretical Probability, 2007, vol. 20, issue 4, 871-899

Abstract: Abstract In this article, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H. We consider two cases. If H>1/2, the exact rate of convergence of the Euler scheme is determined. We show that the error of the Euler scheme converges almost surely to a random variable, which in particular depends on the Malliavin derivative of the solution. This result extends those contained in J. Complex. 22(4), 459–474, 2006 and C.R. Acad. Sci. Paris, Ser. I 340(8), 611–614, 2005. When 1/6

Keywords: Fractional Brownian motion; Russo-Vallois integrals; Doss-Sussmann type transformation; Stochastic differential equations; Euler scheme; Crank-Nicholson scheme; Mixing law (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-007-0083-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:20:y:2007:i:4:d:10.1007_s10959-007-0083-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-007-0083-0

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().