Theoretical statistics for stochastic processes and limit theorems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340015
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo
• Principal Investigator: Yoshida Nakahiro 東京大学, 数理(科)学研究科(研究院), 教授 (90210707)
• Co-Investigator(Kenkyū-buntansha): MASUDA Hiroki 九州大学, 大学院数理学研究院, 教授 (10380669)
• Co-Investigator(Renkei-kenkyūsha): MURATA Noboru 早稲田大学, 理工学術院, 教授 (60242038) ; UCHIDA Masayuki 大阪大学, 大学院基礎工学研究科, 教授 (70280526) ; SHIMIZU Yasutaka 早稲田大学, 理工学術院, 准教授 (70423085) ; FUKASAWA Masaaki 大阪大学, 大学院基礎工学研究科, 教授 (70506451) ; KAMATANI Kengo 大阪大学, 大学院基礎工学研究科, 講師 (00569767)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 漸近展開 / Malliavin解析 / 極限定理 / 確率過程の統計学 / 擬似尤度解析 / 非同期共分散推定 / ボラティリティ / セミマルチンゲール

Outline of Final Research Achievements

The quasi likelihood analysis was constructed for a stochastic regression model of volatility based on high frequency data in the finite time horizon, and an analytic criterion and a geometric criterion for non-degeneracy of the statistical random field associated with the quasi likelihood function were provided. The asymptotic mixed normality and the convergence of moments were proved. A quasi likelihood analysis was developed for a non-synchronously observed stochastic differential equation. Asymptotic expansion for a martingale with mixed normal limit was established. It is a new limit theorem beyond the frame of the present theory of asymptotic expansion for ergodic processes. The martingale expansion was applied to the p-variation. Studies of the asymptotic expansion of volatility estimators under microstructure noise have been developed. The spot volatility information criterion sVIC was proposed, and the fundamentals for developing computer software were studied.

Free Research Field

確率統計学