We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with the quadratic covariation of the latent random process that drives the evolution equation which is assumed to be a Hilbert space-valued semimartingale. We discuss applications to dynamically consistent and outlier-robust dimension reduction in the spirit of functional principal components and the estimation of infinite-dimensional stochastic volatility models.

翻译：我们针对无限维随机演化方程中的协变差跳跃稳健测量发展了一套渐近理论。具体而言，我们建立了求解过程实现协变差的标度极限与驱动演化方程的潜在随机过程（假设为希尔伯特空间值半鞅）的二次协变差之间的对应关系。我们探讨了该理论在泛函主成分思想指导下的动态一致且离群值稳健的降维应用，以及无限维随机波动率模型的估计问题。