HIGH-FREQUENCY ANALYSIS OF PARABOLIC STOCHASTIC PDES

• 成果类型: Article
• 署名作者: Chong, Carsten
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1841
• 发表日期: 2020
• 页码: 1143-1167
• 关键词: ornstein-uhlenbeck processes; LIMIT-THEOREMS; power variations; MODEL; SPACE; volatility; EQUATIONS; BEHAVIOR; driven; jumps

摘要

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at 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.