论文标题
在希尔伯特空间环境中实现的协方差的大量法律薄弱
A weak law of large numbers for realised covariation in a Hilbert space setting
论文作者
论文摘要
本文概括了实现协方差与希尔伯特空间价值随机过程的概念。更确切地说，基于高频功能数据，我们构建了trace级操作员价值的综合波动过程的估计器，该过程在Hilbert太空价值随机进化方程的一般轻度溶液中产生，其意义是Da Prato和Zabczyk（2014）。对于此估计值，我们证明了大数量的薄弱法则，其中相对于Hilbert-Schmidt Norm，在紧凑的概率上，收敛性均匀。此外，我们表明，波动率过程的条件对于希尔伯特空间中最常见的随机波动率模型有效。
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated volatility process arising in general mild solutions of Hilbert space-valued stochastic evolution equations in the sense of Da Prato and Zabczyk (2014). We prove a weak law of large numbers for this estimator, where the convergence is uniform on compacts in probability with respect to the Hilbert-Schmidt norm. In addition, we show that the conditions on the volatility process are valid for most common stochastic volatility models in Hilbert spaces.
