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Infinite dimensional forward-backward stochastic differential equations and the KPZ equation

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Infinite dimensional forward-backward stochastic differential equations and the KPZ equation
2.	Creator	Author's name, affiliation, country	Sergio Almada Monter; UNC Chapel Hill; United States
2.	Creator	Author's name, affiliation, country	Amarjit Budhiraja; UNC Chapel Hill; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	KPZ Equation, Backward SDE, Feynman-Kac
3.	Subject	Subject classification	60H15,
4.	Description	Abstract	Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation (SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of this equation. Bertini, Cancrini and Giacomin have proposed a notion of a solution through a limiting procedure and a certain renormalization of the nonlinearity. In this work we study connections between the KPZ equation and certain infinite dimensional forward-backward stochastic differential equations. Forward-backward equations with a finite dimensional noise have been studied extensively, mainly motivated by problems in mathematical finance. Equations considered here differ from the classical works in that, in addition to having an infinite dimensional driving noise, the associated SPDE involves a non-Lipschitz (specifically, a quadratic) function of the gradient. Existence and uniqueness of solutions of such infinite dimensional forward-backward equations is established and the terminal values of the solutions are then used to give a new probabilistic representation for the solution of the KPZ equation.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2014-04-04
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/2709
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2709
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.)
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