LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY  

作　　者：Zhongmin QIAN Xingcheng XU 钱忠民;徐兴成(Mathematical Institute,University of Oxford,Oxford,OX26GG,UK;Shanghai Artificial Intelligence Laboratory,Shanghai,200232,China;School of Mathematical Sciences,Peking University,Beijing,100871,China)

机构地区：[1]Mathematical Institute,University of Oxford,Oxford,OX26GG,UK [2]Shanghai Artificial Intelligence Laboratory,Shanghai,200232,China [3]School of Mathematical Sciences,Peking University,Beijing,100871,China

出　　处：《Acta Mathematica Scientia》2024年第5期1609-1638,共30页数学物理学报（B辑英文版）

基　　金：supported by Shanghai Artificial Intelligence Laboratory.

摘　　要：This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.

关 键 词：Itôintegration Lévy area non-geometric rough path fOU processes pathwise stability long time asymptotic high-frequency data 

分 类 号：O211.6[理学—概率论与数理统计]