Mixed sub-fractional Brownian motion and drift estimation of related Ornstein-Uhlenbeck process

2018/09/05 by Chunhao Cai, Cai, Chunhao, Qinghua Wang +3 · 1 citation
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1809.02038

openalex publication_date 2018/09/05 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28

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.

Cited by

• Parameter estimation for an Ornstein-Uhlenbeck Process driven by a general Gaussian noise with Hurst Parameter H∈ (0,\frac12)

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