论文标题
由仅空间噪声驱动的离散采样随机热方程的参数估计
Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise
论文作者
论文摘要
当在物理域中离散地对溶液进行离散采样时，我们为随机热方程的漂移和挥发性参数提供一致和渐近正常的估计器。我们考虑整个空间和有限域。我们建立了解决方案的确切空间规律性，进而使用功率变化参数允许构建所需的估计器。我们表明，基于功率变化的估计器中出现的衍生物的天真近似可能会产生非平凡的偏见，我们明确地计算出来。证明植根于Malliavin-Stein的方法。
We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain. We consider both the full space and the bounded domain. We establish the exact spatial regularity of the solution, which in turn, using power-variation arguments, allows building the desired estimators. We show that naive approximations of the derivatives appearing in the power-variation based estimators may create nontrivial biases, which we compute explicitly. The proofs are rooted in Malliavin-Stein's method.
