A note on inference for the mixed fractional Ornstein-Uhlenbeck process with drift

Chunhao Cai; Min Zhang; Chunhao Cai; Min Zhang

doi:10.3934/math.2021378

AIMS Mathematics

2021, Volume 6, Issue 6: 6439-6453. doi: 10.3934/math.2021378

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Research article

A note on inference for the mixed fractional Ornstein-Uhlenbeck process with drift

Chunhao Cai ^,,
Min Zhang

School of Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, 200433, China

Received: 08 February 2021 Accepted: 08 April 2021 Published: 14 April 2021
MSC : 60G22, 62F10

This paper is devoted to the controlled drift estimation of the mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one is the optimal input where we will find the controlled function which maximize the Fisher information for the unknown parameter and the other one with a constant as the controlled function. Large sample asymptotical properties of the Maximum Likelihood Estimator (MLE) is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from ^[12]. As a a supplement of ^[12] we will also prove that the MLE is strongly consistent.
- mixed fractional Brownian motion,
- fundamental martingale,
- Laplace transform,
- optimal input
Citation: Chunhao Cai, Min Zhang. A note on inference for the mixed fractional Ornstein-Uhlenbeck process with drift[J]. AIMS Mathematics, 2021, 6(6): 6439-6453. doi: 10.3934/math.2021378

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Abstract

This paper is devoted to the controlled drift estimation of the mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one is the optimal input where we will find the controlled function which maximize the Fisher information for the unknown parameter and the other one with a constant as the controlled function. Large sample asymptotical properties of the Maximum Likelihood Estimator (MLE) is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from ^[12]. As a a supplement of ^[12] we will also prove that the MLE is strongly consistent.

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