Glivenko-Cantelli Theorems for integrated functionals of stochastic processes

• Main Authors: LI, Jia, ZHANG, Congshan, LIU, Yunxiao
• 格式: text
• 語言: English
• 出版: Institutional Knowledge at Singapore Management University 2021
• 主題: Glivenko-Cantelli; high-frequency data; spot volatility; microstructure noise; occupation measure; Econometrics; Probability
• 在線閱讀: https://ink.library.smu.edu.sg/soe_research/2535; https://ink.library.smu.edu.sg/context/soe_research/article/3534/viewcontent/gc_aos.pdf
• 機構: Singapore Management University

We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced b...