Well-posedness and Large Deviations of the Stochastic Modified Camassa-Holm Equation

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• 作者：Yong Chen ; Hongjun Gao
• 刊名：Potential Analysis
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：45
• 期：2
• 页码：331-354
• 全文大小：493 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：45

文摘

In this paper, the stochastic modified Camassa-Holm (MCH) equation is concerned. Firstly, the local well-posedness for this equation is established by the trilinear estimates to the approximate solutions. Then the large deviation principle (LDP) for the regularized stochastic MCH is obtained by the weak convergence approach. To get the LDP for stochastic MCH, some exponentially equivalents of the probability measures are proved. The regularization method plays an crucial role.KeywordsStochastic modified Camassa-Holm equationWell-posednessLarge deviationsRegulationTrilinear estimate