Numerical Schemes for Rough Parabolic Equations

被引：5
|
作者：
Deya, Aurelien [1 ]
机构：
[1] Univ Nancy 1, Inst Elie Cartan Nancy, F-54506 Vandoeuvre Les Nancy, France
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2012年 / 65卷 / 02期
关键词：
Rough paths theory; Stochastic PDEs; Approximation schemes; Fractional Brownian motion; PARTIAL-DIFFERENTIAL-EQUATIONS; STOCHASTIC-EVOLUTION EQUATIONS; FRACTIONAL BROWNIAN-MOTION; TAYLOR EXPANSIONS; ADDITIVE NOISE; DRIVEN; TIME; APPROXIMATION; SIMULATION; PATHS;
D O I：
10.1007/s00245-011-9157-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H > 1/3.
引用
收藏
页码：253 / 292
页数：40
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