Optimal rate of convergence for stochastic Burgers-type equations

被引：10

作者：

Hairer, M. ^{[1
]}

Matetski, K. ^{[1
]}

机构：

[1] Univ Warwick, Math Dept, Coventry, W Midlands, England

来源：

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2016年 / 4卷 / 02期

关键词：

Burgers equation; Approximations; Rough paths;

D O I：

10.1007/s40072-015-0067-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, a solution theory for one-dimensional stochastic PDEs of Burgers type driven by space-time white noise was developed. In particular, it was shown that natural numerical approximations of these equations converge and that their convergence rate in the uniform topology is arbitrarily close to 16. In the present article we improve this result in the case of additive noise by proving that the optimal rate of convergence is arbitrarily close to 1/2

引用

页码：402 / 437

页数：36

共 30 条

[1] On numerical approximation of stochastic Burgers' equation [J].

Alabert, A ;

Gyöngy, I .

FROM STOCHASTIC CALCULUS TO MATHEMATICAL FINANCE: THE SHIRYAEV FESTSCHRIFT, 2006, :1-+

[2]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[3] GALERKIN APPROXIMATIONS FOR THE STOCHASTIC BURGERS EQUATION [J].

Bloemker, Dirk ;

Jentzen, Arnulf .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (01) :694-715

[4]

Chen K.-T., 1954, P LOND MATH SOC, V4, P502

[5]

Da Prato G., 2002, LONDON MATH SOC LECT, DOI [10.1017/CBO9780511543210, DOI 10.1017/CBO9780511543210]

[6]

Davie AM, 2001, MATH COMPUT, V70, P121, DOI 10.1090/S0025-5718-00-01224-2

[7]

Friz P., 2010, THEORY APPL CAMBRIDG, V120

[8]

Friz P. K., 2013, ARXIV13073460V2

[9] Controlling rough paths [J].

Gubinelli, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 216 (01) :86-140

[10]

Gubinelli M., 2012, ARXIV12102684

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