Glivenko-Cantelli Theorems for integrated functionals of stochastic processes

• المؤلفون الرئيسيون: LI, Jia, ZHANG, Congshan, LIU, Yunxiao
• التنسيق: text
• اللغة: English
• منشور في: Institutional Knowledge at Singapore Management University 2021
• الموضوعات: Glivenko-Cantelli; high-frequency data; spot volatility; microstructure noise; occupation measure; Econometrics; Probability
• الوصول للمادة أونلاين: https://ink.library.smu.edu.sg/soe_research/2535; https://ink.library.smu.edu.sg/context/soe_research/article/3534/viewcontent/gc_aos.pdf
• المؤسسة: 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...