A PDE approach to large deviations in Hilbert spaces

被引：4

作者：

Swiech, Andrzej ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 04期

关键词：

Large deviations; Viscosity solutions; Hamilton-Jacobi-Bellman equations; Stochastic PDE; Stochastic Navier-Stokes equations; NAVIER-STOKES EQUATIONS; PARTIAL-DIFFERENTIAL-EQUATIONS; HAMILTON-JACOBI EQUATIONS; UNBOUNDED LINEAR TERMS; VISCOSITY SOLUTIONS; INFINITE DIMENSIONS; MULTIPLICATIVE NOISE; BELLMAN EQUATIONS; PERTURBATIONS;

D O I：

10.1016/j.spa.2008.05.005

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：

We introduce a PDE approach to the large deviation principle for Hilbert space valued diffusions. It can be applied to a large class of solutions of abstract stochastic evolution equations with small noise intensities and is adaptable to some special equations, for instance to the 2D stochastic Navier-Stokes equations. Our approach uses a lot of ideas from (and in significant part follows) the program recently developed by Feng and Kurtz [J. Feng, T. Kurtz, Large Deviations for Stochastic Processes, in: Mathematical Surveys and Monographs, vol. 13], American Mathematical Society, Providence, RI, 2006]. Moreover we present easy proofs of exponential moment estimates for solutions of stochastic FIDE. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1081 / 1123

页数：43

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