Scholarlink

<p>We study the problem of parametric estimation for continuously observed stochastic differential equation driven by an <i>r</i>–dimensional fractional Brownian motion with possibly different Hurst indices <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_i\in (1/3,1/2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>∈</mo> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>3</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood estimator and establish its asymptotic normality and moment convergence of the drift parameter when a small dispersion coefficient <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</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

The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case

  • 期刊论文

  • 发表日期：

    2025年12月1日

查看全文
  • Shohei Nakajima

摘要

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by an r–dimensional fractional Brownian motion with possibly different Hurst indices \(H_i\in (1/3,1/2)\) H i ∈ ( 1 / 3 , 1 / 2 ) . Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood estimator and establish its asymptotic normality and moment convergence of the drift parameter when a small dispersion coefficient \(\varepsilon \rightarrow 0\) ε → 0 .