High-frequency analysis of parabolic stochastic PDEs
High-frequency analysis of parabolic stochastic PDEs
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DOI：
10.1214/19-aos1841
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发表时间：
2018-06
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影响因子：
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通讯作者：
Carsten Chong
中科院分区：
文献类型：
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作者：
Carsten Chong
我们考虑估计一类二阶抛物线随机偏微分方程的随机波动性的问题。假设在高时间频率下观察到解，我们使用多幂变化的极限定理和相关泛函来构造积分波动率过程的一致非参数估计量和渐近置信界。作为我们分析的副产品，我们还获得了噪声空间协方差函数规律性的可行估计量。
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of the noise.