Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

被引：17

作者：

Becker, Sebastian ^{[1
]}

Gess, Benjamin ^{[2
,3
]}

Jentzen, Arnulf ^{[4
,5
,6
,7
]}

Kloeden, Peter E. ^{[8
]}

机构：

[1] Swiss Fed Inst Technol, RiskLab, Dept Math, CH-8092 Zurich, Switzerland

[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[3] Univ Bielefeld, Fac Math, D-33615 Bielefeld, Germany

[4] Chinese Univ Hong Kong, Sch Data Sci, Shenzhen 518172, Peoples R China

[5] Chinese Univ Hong Kong, Shenzhen Res Inst Big Data, Shenzhen 518172, Peoples R China

[6] Univ Munster, Appl Math Inst Anal & Numer, D-48149 Munster, Germany

[7] Swiss Fed Inst Technol, Dept Math, Seminar Appl Math, CH-8092 Zurich, Switzerland

[8] Goethe Univ Frankfurt, Math Inst, D-60325 Frankfurt, Germany

来源：

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS | 2023年 / 11卷 / 01期

关键词：

Stochastic partial differential equation; SPDE; Stochastic Allen-Cahn equation; Numerical method; Numerical approximation; Strong convergence; DISCRETIZATION; COEFFICIENTS; SCHEMES; BOUNDS; SPDES; LIMIT; SDES;

D O I：

10.1007/s40072-021-00226-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Strong convergence rates for fuly discrete numerical approximations of space-time white noise driven SPDEs with superlinearly growing nonlinearities, such as the stochastic Allen-Cahn equation with space-time white noise, are shown. The obtained strong rates of convergence are essentially sharp.

引用

页码：211 / 268

页数：58

共 40 条

[1] Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values [J].

Andersson, Adam ;

Jentzen, Arnulf ;

Kurniawan, Ryan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (01)

[2] Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients [J].

不详 .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 236 (1112) :1-+

[3]

[Anonymous], 2014, Encyclopedia of Mathematics and Its Applications

[4]

Becker S., 2017, ARXIV171102423V1

[5] Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations [J].

Becker, Sebastian ;

Gess, Benjamin ;

Jentzen, Arnulf ;

Kloeden, Peter E. .

BIT NUMERICAL MATHEMATICS, 2020, 60 (04) :1057-1073

[6] Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations [J].

Becker, Sebastian ;

Jentzen, Arnulf .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (01) :28-69

[7] Modulation Equation and SPDEs on Unbounded Domains [J].

Bianchi, Luigi Amedeo ;

Bloemker, Dirk ;

Schneider, Guido .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2019, 371 (01) :19-54

[8] Numerically computable a posteriori-bounds for the stochastic Allen-Cahn equation [J].

Bloemker, Dirk ;

Kamrani, Minoo .

BIT NUMERICAL MATHEMATICS, 2019, 59 (03) :647-673

[9] Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation [J].

Brehier, Charles-Edouard ;

Goudenege, Ludovic .

BIT NUMERICAL MATHEMATICS, 2020, 60 (03) :543-582

[10] ANALYSIS OF SOME SPLITTING SCHEMES FOR THE STOCHASTIC ALLEN-CAHN EQUATION [J].

Brehier, Charles-Edouard ;

Goudenege, Ludovic .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08) :4169-4190

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