| 分式噪声驱动的一类随机偏微分方程的非参数估计} |
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| 引用本文： | 唐丹,王永进,张冠男.分式噪声驱动的一类随机偏微分方程的非参数估计}[J].数学年刊A辑(中文版),2013,34(5):627-642. |
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| 作者姓名： | 唐丹 王永进 张冠男 |
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| 作者单位： | 对外经济贸易大学国际经济贸易学院, 北京 100029.;南开大学商学院和数学科学学院, 天津 300071.;南开大学数学科学学院, 天津 300071. |
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| 基金项目： | 国家自然科学基金 (No.11101083)和对外经济贸易大学学术创新团队资助项目(数量经济学理论与应用创新团队)(No.CXTD4-01) |
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| 摘 要： | 研究了一类由分式噪声所驱动的随机偏微分方程的统计推断. 先构造了偏微分算子时间
相依系数的非参数估计量, 然后得到了该估计在最大值范数下的收敛率和渐近正态性. 该收敛率
由系数的平滑参数和分式噪声的Hurst参数共同决定.
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| 关 键 词： | 分式噪声 非参数统计 随机偏微分方程 |
Nonparametric Inference for a Class of SPDEs Driven by Fractional Noises |
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| TANG Dan,WANG Yongjin and ZHANG Guannan.Nonparametric Inference for a Class of SPDEs Driven by Fractional Noises[J].Chinese Annals of Mathematics,2013,34(5):627-642. |
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| Authors: | TANG Dan WANG Yongjin and ZHANG Guannan |
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| Institution: | School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China.;School of Business and School of Mathematical Sciences, Nankai University,
Tianjin 300071, China.;School of Mathematical Sciences, Nankai University,
Tianjin 300071, China. |
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| Abstract: | The nonparametric inference for a class of stochastic partial differential equations
driven by fractional noises is investigated. The authors construct a non-parametric estimator
of the time-dependent coefficient of the partial differential operator. The convergence in the
sup-norm and asymptotic normality of the estimator are established. The rate of convergence
is determined by both the smoothness of the coefficient and the Hurst parameter of the
fractional noise. |
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| Keywords: | Fractional noise Nonparametric inference Stochastic partial
differential equation |
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