Abstract We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency data, adaptive estimators of the coefficient parameters including the volatility parameter are proposed. Moreover, we give some examples and simulation results of the adaptive estimators of the SPDE model based on the high frequency data.

中文翻译：

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基于离散观测的抛物线线性 SPDE 模型的参数估计

摘要 我们考虑从在时间和空间中观察到的高频数据对抛物线线性二阶随机偏微分方程 (SPDE) 进行参数估计。通过使用从高频数据中获得的细化数据，提出了包括波动率参数在内的系数参数的自适应估计器。此外，我们给出了一些基于高频数据的SPDE模型自适应估计器的例子和仿真结果。