We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptotic regime. The asymptotic variances are shown to be substantially smaller compared to existing estimation methods. Moreover, asymptotic confidence intervals are directly feasible. Our approach builds upon realized volatilities and their asymptotic illustration as response of a log-linear model with spatial explanatory variable. This yields efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. We demonstrate efficiency gains compared to previous estimation methods numerically and in Monte Carlo simulations.

翻译：我们根据对时间和空间上封闭域上溶液的离散观测,为抛射式SPDE参数建立一个空间层面的测算器。我们为高频无药可治系统设定了中心限理论。与现有估算方法相比,无药可治差异明显小得多。此外,无药可治的置信间隔直接可行。我们的方法以已实现的挥发性及其无药可治性图解为基础,作为带有空间解释变量的对线模型的响应。这产生基于最佳趋同率和最小差异的已实现挥发性的有效估测器。我们展示了与以往估算方法相比的效率增益,以及在蒙特卡洛模拟中也显示了效率增益。