数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 2064-2076.doi: 10.1016/S0252-9602(10)60191-9

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EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

任剑1, 付红波1, 曹道民2, 段金桥3, 1   

  1. 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
    2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, China
    3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
  • 收稿日期:2010-09-08 出版日期:2010-11-20 发布日期:2010-11-20
  • 基金资助:

    This work was partly supported by   NSF of China (10901065, 10971225, and 11028102), the NSF Grants 1025422 and 0731201, the Cheung Kong Scholars Program, and an open research grant from the State Key Laboratory for Nonlinear Mechanics at the Chinese Academy of Sciences.

EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

 REN Jian1, FU Hong-Bo1, CAO Dao-Min2, DUAN Jin-Qiao3, 1   

  1. 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
    2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, China
    3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
  • Received:2010-09-08 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    This work was partly supported by   NSF of China (10901065, 10971225, and 11028102), the NSF Grants 1025422 and 0731201, the Cheung Kong Scholars Program, and an open research grant from the State Key Laboratory for Nonlinear Mechanics at the Chinese Academy of Sciences.

摘要:

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.

关键词: microscopic-macroscopic system, stochastic partial differential equations,  averaging principle, effective dynamics, slow-fast scales

Abstract:

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.

Key words: microscopic-macroscopic system, stochastic partial differential equations,  averaging principle, effective dynamics, slow-fast scales

中图分类号: 

  • 60H15