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<p>In this paper, we study asymptotic behavior of small perturbation for path-distribution dependent stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H \in ({1 \over 2}, 1)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>H</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> and a standard Brownian motion. We establish large and moderate deviation principles by utilising the weak convergence approach.</p>

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Large and Moderate Deviation Principles for Path-Distribution Dependent SDEs Driven by Mixed Fractional Brownian Motion

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Guangjun Shen,
  • Huan Zhou,
  • Jiang-Lun Wu

摘要

In this paper, we study asymptotic behavior of small perturbation for path-distribution dependent stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter \(H \in ({1 \over 2}, 1)\) H ∈ ( 1 2 , 1 ) and a standard Brownian motion. We establish large and moderate deviation principles by utilising the weak convergence approach.