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Propagating Lyapunov functions to prove noise-induced stabilization

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Propagating Lyapunov functions to prove noise-induced stabilization
2.	Creator	Author's name, affiliation, country	Avanti Athreya; The Johns Hopkins University; United States
2.	Creator	Author's name, affiliation, country	Tiffany Kolba; Valparaiso University; United States
2.	Creator	Author's name, affiliation, country	Jonathan C Mattingly; Duke University; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	SDEs, Lyapunov Functions, Invariant Measures, Stochastic Stabilization
3.	Subject	Subject classification	37A25;37A30;37B25;60H10
4.	Description	Abstract	We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the addition of additive noise in the vertical direction leads to a unique invariant probability measure to which the system converges at a uniform, exponential rate. These facts are established primarily through the construction of a Lyapunov function which we generate as the solution to a sequence of Poisson equations. Unlike a number of other works, however, our Lyapunov function is constructed in a systematic way, and we present a meta-algorithm we hope will be applicable to other problems. We conclude by proving positivity properties of the transition density by using Malliavin calculus via some unusually explicit calculations.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2012-11-02
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/2410
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2410
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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