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<p>In this paper, we study the asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion in infinite dimensions. We first establish large and moderate deviation principles for the considered equations by fully utilizing the weak convergence method and fractional calculus. Besides, we present the central limit theorem, i.e., the deviation between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X^{\epsilon }(t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>X</mi> <mi>ϵ</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X^{0}(t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>X</mi> <mn>0</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> converges weakly to a limiting process.</p>

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Asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Huan Zhou,
  • Guangjun Shen

摘要

In this paper, we study the asymptotic behaviors for distribution dependent stochastic partial differential equations driven by fractional Brownian motion in infinite dimensions. We first establish large and moderate deviation principles for the considered equations by fully utilizing the weak convergence method and fractional calculus. Besides, we present the central limit theorem, i.e., the deviation between \(X^{\epsilon }(t)\) X ϵ ( t ) and \(X^{0}(t)\) X 0 ( t ) converges weakly to a limiting process.