ECP Reading Tools

A modified Kardar-Parisi-Zhang model

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A modified Kardar-Parisi-Zhang model
2.	Creator	Author's name, affiliation, country	Giuseppe Da Prato; Scuola Normale Superiore PISA Italy
2.	Creator	Author's name, affiliation, country	Arnaud Debussche; IRMAR, ENS Cachan Bretagne, CNRS, UEB
2.	Creator	Author's name, affiliation, country	Luciano Tubaro; Dipartimento di Matematica, Università di Trento
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stochastic partial differential equations; white noise; invariant measure; Wick product
3.	Subject	Subject classification	60H15; 81S20
4.	Description	Abstract	A one dimensional stochastic differential equation of the form \[dX=A X dt+\tfrac12 (-A)^{-\alpha}\partial_\xi[((-A)^{-\alpha}X)^2]dt+\partial_\xi dW(t),\qquad X(0)=x\] is considered, where $A=\tfrac12 \partial^2_\xi$. The equation is equipped with periodic boundary conditions. When $\alpha=0$ this equation arises in the Kardar-Parisi-Zhang model. For $\alpha\ne 0$, this equation conserves two important properties of the Kardar-Parisi-Zhang model: it contains a quadratic nonlinear term and has an explicit invariant measure which is gaussian. However, it is not as singular and using renormalization and a fixed point result we prove existence and uniqueness of a strong solution provided $\alpha>\frac18$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2007-11-28
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/1333
10.	Identifier	Digital Object Identifier	10.1214/ECP.v12-1333
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 12
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.