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

被引:0
|
作者
Monter, Sergio A. Almada [1 ]
Budhiraja, Amarjit [1 ]
机构
[1] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27514 USA
来源
ELECTRONIC JOURNAL OF PROBABILITY | 2014年 / 19卷
基金
美国国家科学基金会;
关键词
Kardar-Parisi-Zhang equation; infinite dimensional noise; Backward stochastic differential equations; nonlinear stochastic partial differential equations; probabilistic representations; PARTICLE;
D O I
10.1214/EJP.v19-2709
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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 [2, 3] 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.
引用
收藏
页码:1 / 21
页数:21
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