分式噪声驱动的一类随机偏微分方程的非参数估计

Nonparametric Inference for a Class of SPDEs Driven by Fractional Noises

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.

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.