ECP Reading Tools

Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
2.	Creator	Author's name, affiliation, country	Jeremie M Unterberger; Institut Elie Cartan de Nancy - Universite Henri Poincare - Nancy (France)
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stochastic differential equations, fractional Brownian motion, analytic fractional Brownian motion, rough paths, H"older continuity, Chen series
3.	Subject	Subject classification	60G15, 60H05, 60H10
4.	Description	Abstract	As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition - and also estimates - of the solutions depend on upper bounds for the rough path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with Holder regularity $\alpha<1/2$. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [6,7] with arbitrary Hurst index $\alpha\in(0,1)$ may be solved on the closed upper half-plane, and that the solutions have finite variance.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-09-30
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1574
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1574
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.