论文标题
路径的最小二乘估计器的线性SPDE具有添加剂分数噪声
Pathwise least-squares estimator for linear SPDEs with additive fractional noise
论文作者
论文摘要
本文通过最小二乘过程介绍了带有分数噪声的线性随机演化方程（强调线性SPDE）的漂移估计（重点是线性SPDE）（赫斯特索引范围为0到1）。由于最小二乘估计量包含差异类型的随机积分，因此我们通过与Stratonovich类型的路径积分和使用其链条规则属性进行比较，解决了其路径方向（以及鲁棒与观察误差）评估的问题。然后将所得的路径LSE隐式定义为非线性方程的解决方案。我们研究其数值特性（解决方案的存在和唯一性）以及统计特性（强度一致性和收敛的速度）。假设观察到的傅立叶模式（空间渐近性）的数量增加，则获得渐近特性。我们还猜想了途径LSE的渐近正态性。
This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares estimator contains stochastic integrals of divergence type, we address the problem of its pathwise (and robust to observation errors) evaluation by comparison with the pathwise integral of Stratonovich type and using its chain-rule property. The resulting pathwise LSE is then defined implicitly as a solution to a non-linear equation. We study its numerical properties (existence and uniqueness of the solution) as well as statistical properties (strong consistency and the speed of its convergence). The asymptotic properties are obtained assuming fixed time horizon and increasing number of the observed Fourier modes (space asymptotics). We also conjecture the asymptotic normality of the pathwise LSE.
