Averaging principle for two-time-scale stochastic differential equations with correlated noise

被引：0

作者：

Jiang, Tao ^{[2
]}

Liu, Yancai ^{[1
]}

机构：

[1] Henan Univ Technol, Sch Sci, Zhengzhou 450001, Peoples R China

[2] Hubei Univ Econ, Hubei Ctr Data & Anal, Wuhan 430205, Peoples R China

来源：

OPEN MATHEMATICS | 2022年 / 20卷 / 01期

基金：

中国国家自然科学基金;

关键词：

averaging principle; stochastic differential equation; correlated noise; multiscale expansion; HYPERBOLIC-PARABOLIC EQUATIONS; DIFFUSION-APPROXIMATION; STRONG-CONVERGENCE; POISSON-EQUATION; SYSTEMS; DRIVEN;

D O I：

10.1515/math-2022-0538

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article is devoted to studying the averaging principle for two-time-scale stochastic differential equations with correlated noise. By the technique of multiscale expansion of the solution to the backward Kolmogorov equation and consequent elimination of variables, we obtain the Kolmogorov equation corresponding to the reduced simplified system. The approximation of the slow component of the original system to the solution of the corresponding averaged equation is in the weak sense. An example is also provided to illustrate our result.

引用

页码：1656 / 1664

页数：9

共 26 条

[1] Two-time-scale stochastic partial differential equations driven by α-stable noises: Averaging principles [J].

Bao, Jianhai ;

Yin, George ;

Yuan, Chenggui .

BERNOULLI, 2017, 23 (01) :645-669

[2]

Bogoliubov NN., 1961, Asymptotic Methods in the Theory of Nonlinear Oscillations

[3] Strong and weak orders in averaging for SPDEs [J].

Brehier, Charles-Edouard .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (07) :2553-2593

[4] AVERAGING PRINCIPLE FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS WITH POLYNOMIAL NONLINEARITIES PERTURBED BY MULTIPLICATIVE NOISE [J].

Cerrai, Sandra .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (06) :2482-2518

[5] A KHASMINSKII TYPE AVERAGING PRINCIPLE FOR STOCHASTIC REACTION-DIFFUSION EQUATIONS [J].

Cerrai, Sandra .

ANNALS OF APPLIED PROBABILITY, 2009, 19 (03) :899-948

[6] Averaging principle for a class of stochastic reaction-diffusion equations [J].

Cerrai, Sandra ;

Freidlin, Mark .

PROBABILITY THEORY AND RELATED FIELDS, 2009, 144 (1-2) :137-177

[7] Long-time behavior of weakly coupled oscillators [J].

Freidlin, M. I. ;

Wentzell, A. D. .

JOURNAL OF STATISTICAL PHYSICS, 2006, 123 (06) :1311-1337

[8] Strong convergence in averaging principle for stochastic hyperbolic-parabolic equations with two time-scales [J].

Fu, Hongbo ;

Wan, Li ;

Liu, Jicheng .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (08) :3255-3279

[9] AN AVERAGING PRINCIPLE FOR TWO-SCALE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS [J].

Fu, Hongbo ;

Duan, Jinqiao .

STOCHASTICS AND DYNAMICS, 2011, 11 (2-3) :353-367

[10] Strong convergence in stochastic averaging principle for two time-scales stochastic partial differential equations [J].

Fu, Hongbo ;

Liu, Jicheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 384 (01) :70-86

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