Mixed Sub-fractional Brownian Motion and Drift Estimation of Related Ornstein–Uhlenbeck Process

Abstract

In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein–Uhlenbeck process, and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter $H>1/2$.

Keywords

Sub-fractional Brownian motion / Ornstein–Uhlenbeck process / Least square estimator / Malliavin calculus

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Funding

Shanghai University of Finance and Economics(2020110294)

National Natural Science Foundation of China(71871202)