Large deviations for stochastic heat equation with rough dependence in space

被引：8

作者：

Hu, Yaozhong ^{[1
]}

Nualart, David ^{[1
]}

Zhang, Tusheng ^{[2
]}

机构：

[1] Univ Kansas, Dept Math, 405 Snow Hall, Lawrence, KS 66045 USA

[2] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

来源：

BERNOULLI | 2018年 / 24卷 / 01期

基金：

美国国家科学基金会;

关键词：

fractional Brownian motion; large deviations; stochastic heat equation;

D O I：

10.3150/16-BEJ880

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：

In this paper, we establish a large deviation principle for the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (1/4,1/2) in the space variable.

引用

页码：354 / 385

页数：32

共 17 条

[1]

[Anonymous], ELECT J PROBAB

[2] SPDEs with affine multiplicative fractional noise in space with index 1/4 < H < 1/2 [J].

Balan, Raluca M. ;

Jolis, Maria ;

Quer-Sardanyons, Lluis .

ELECTRONIC JOURNAL OF PROBABILITY, 2015, 20 :1-36

[3]

Budhiraja A., 2000, PROBAB MATH STAT-POL, V20, P139

[4] Large deviations for infinite dimensional stochastic dynamical systems [J].

Budhiraja, Amarjit ;

Dupuis, Paul ;

Maroulas, Vasileios .

ANNALS OF PROBABILITY, 2008, 36 (04) :1390-1420

[5] Uniform large deviations for parabolic SPDEs and applications [J].

Chenal, F ;

Millet, A .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 72 (02) :161-186

[6] Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations [J].

Chueshov, Igor ;

Millet, Annie .

APPLIED MATHEMATICS AND OPTIMIZATION, 2010, 61 (03) :379-420

[7]

Da Prato G., 2014, STOCHASTIC EQUATIONS, P152, DOI [10.1017/CBO9780511666223, 10.1017/CBO9781107295513]

[8] Stochastic integrals for spde's: A comparison [J].

Dalang, Robert C. ;

Quer-Sardanyons, Lluis .

EXPOSITIONES MATHEMATICAE, 2011, 29 (01) :67-109

[9]

Dalang Robert C., 1999, ELECTRON J PROBAB, V4, P29, DOI [10.1214/EJP.v4-43, DOI 10.1214/EJP.V4-43]

[10]

Dupuis P., 1997, A Weak Convergence Approach to the Theory of Large Deviations, DOI [10.1002/9781118165904, DOI 10.1002/9781118165904]

← 1 2 →