Statistical analysis of tempo-spatial stochastic integral processes

在项目的更新期间，我们希望推导出具有高斯驱动噪声的抛物型SPDE的新非参数估计方法，其空间协方差比原始项目中考虑的Riesz核更平滑。这是从金融数学的动机，其中一个是关注建模远期利率的期限结构动态与利率衍生证券定价的目标。实证结果表明，利率期限结构的波动在时间上是不规则的，而在时间上是平滑的。基于高频数据，我们要构建一致的和渐近正态的随机波动率（和空间噪声相关指数）的估计证明极限定理的归一化功率变化的随机热方程在这个新的设置。

In the renewal time of the project, we want to derive new nonparametric estimation methods for parabolic SPDEs with a Gaussian driving noise exhibiting a spatial covariance that is smoother than the Riesz kernels considered in the original project. This is motivated from financial mathematics, where one is concerned with modeling term structure dynamics of forward rates with the objective of pricing interest rate derivative securities. Empirical observations suggest that fluctuations of the term structure should be smooth in the time to maturity while irregular in time. Based on high-frequency data, we want to construct consistent and asymptotically normal estimators for stochastic volatility (and the spatial noise correlation index) by proving limit theorems for the normalized power variations of the stochastic heat equation in this new setting.