Scholarlink

<p>This paper deals with the large deviation principle of the fractional stochastic FitzHugh–Nagumo systems on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> with superlinear drift. We first establish the well-posedness and uniform tail-estimates of solutions to the controlled system associated with the original stochastic equations. We then prove the strong convergence of solutions to the controlled system with respect to the weak topology of controls by the method of tail-ends estimates in order to overcome the non-compactness of Sobolev embeddings on unbounded domains. We finally show the large deviation principle of the FitzHugh–Nagumo system by the weak convergence method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Large Deviations of Fractional Stochastic FitzHugh–Nagumo Systems on \({\mathbb {R}}^n\)

  • 期刊论文

  • 发表日期：

    2026年4月10日

查看全文
  • Zhang Chen,
  • Bixiang Wang

摘要

This paper deals with the large deviation principle of the fractional stochastic FitzHugh–Nagumo systems on \(\mathbb {R}^n\) R n with superlinear drift. We first establish the well-posedness and uniform tail-estimates of solutions to the controlled system associated with the original stochastic equations. We then prove the strong convergence of solutions to the controlled system with respect to the weak topology of controls by the method of tail-ends estimates in order to overcome the non-compactness of Sobolev embeddings on unbounded domains. We finally show the large deviation principle of the FitzHugh–Nagumo system by the weak convergence method.