EJP Reading Tools

Quadratic variations for the fractional-colored stochastic heat equation

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Quadratic variations for the fractional-colored stochastic heat equation
2.	Creator	Author's name, affiliation, country	Soledad Torres; Universidad de Valparaíso; Chile
2.	Creator	Author's name, affiliation, country	Ciprian A. Tudor; Université de Lille 1; France
2.	Creator	Author's name, affiliation, country	Frederi G. Viens; Purdue University; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	multiple stochastic integral; stochastic heat equation; fractional Brownian motion; Malliavin calculus; non-central limit theorem; quadratic variation; Hurst parameter; selfsimilarity; statistical estimation
3.	Subject	Subject classification	60F05; 60H05; 60G18
4.	Description	Abstract	Using multiple stochastic integrals and Malliavin calculus, we analyze the quadratic variations of a class of Gaussian processes that contains the linear stochastic heat equation on $\mathbf{R}^{d}$ driven by a non-white noise which is fractional Gaussian with respect to the time variable (Hurst parameter $H$) and has colored spatial covariance of $\alpha $-Riesz-kernel type. The processes in this class are self-similar in time with a parameter $K$ distinct from $H$, and have path regularity properties which are very close to those of fractional Brownian motion (fBm) with Hurst parameter $K$ (in the heat equation case, $K=H-(d-\alpha )/4$ ). However the processes exhibit marked inhomogeneities which cause naive heuristic renormalization arguments based on $K$ to fail, and require delicate computations to establish the asymptotic behavior of the quadratic variation. A phase transition between normal and non-normal asymptotics appears, which does not correspond to the familiar threshold $K=3/4$ known in the case of fBm. We apply our results to construct an estimator for $H$ and to study its asymptotic behavior.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR; CIMFAV; CNCS; CONYCIT; Dipuv; NSF
7.	Date	(YYYY-MM-DD)	2014-08-23
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/2698
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2698
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	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.