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<p>We address statistical inference for linear fractional diffusion processes with random effects in the drift. In particular, we investigate maximum likelihood estimators (MLEs) of the random effect parameters. First of all, we estimate the Hurst parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_414_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> from one single subject. Second, assuming that the Hurst index <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2024_414_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">\(H\in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is known, we derive the MLEs and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects being normally distributed.</p>

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Statistical inference for discretely observed fractional diffusion processes with random effects

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Mohamed El Omari,
  • Hamid El Maroufy,
  • Christiane Fuchs

摘要

We address statistical inference for linear fractional diffusion processes with random effects in the drift. In particular, we investigate maximum likelihood estimators (MLEs) of the random effect parameters. First of all, we estimate the Hurst parameter \(H\in (0,1)\) H ∈ ( 0 , 1 ) from one single subject. Second, assuming that the Hurst index \(H\in (0,1)\) H ∈ ( 0 , 1 ) is known, we derive the MLEs and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects being normally distributed.