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Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit
2.	Creator	Author's name, affiliation, country	Samuel Herrmann; École des Mines Nancy; France
2.	Creator	Author's name, affiliation, country	Julian Tugaut; Université de Nancy; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	self-interacting diffusion; stationary measures; double well potential; perturbed dynamical system; Laplace's method
3.	Subject	Subject classification	60H10; 60J60; 60G10; 41A60
4.	Description	Abstract	Self-stabilizing diffusions are stochastic processes, solutions of nonlinear stochastic differential equation, which are attracted by their own law. This specific self-interaction leads to singular phenomenons like non uniqueness of associated stationary measures when the diffusion moves in some non convex environment (see [5]). The aim of this paper is to describe these invariant measures and especially their asymptotic behavior as the noise intensity in the nonlinear SDE becomes small. We prove in particular that the limit measures are discrete measures and point out some properties of their support which permit in several situations to describe explicitly the whole set of limit measures. This study requires essentially generalized Laplace's method approximations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-07-06
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/842
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-842
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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