The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek model, statistical inference for this process is of great interest. Based on continuous time observations, this paper considers the problem of estimating the drift parameters in the mixed fractional Vasicek model. We will propose the maximum likelihood estimators of the drift parameters in the mixed fractional Vasicek model with the Radon-Nikodym derivative for a mixed fractional Brownian motion. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators have been established for all $H\in(0,1)$, $H\neq 1/2$.
We investigate the asymptotic properties of maximum likelihood estimators of the drift parameter for fractional vasicek model driven by a sub-fractional Brownian motion.
We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are as follows: firstly, two unknown parameters in the model are estimated by the least squares method. Secondly, the strong consistency and the asymptotic distribution of the estimators are studied respectively. Finally, our estimators are validated by numerical simulation.
This paper developed an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and the asymptotic normality. Our approach extended the result of Xiao and Yu (2018) for the case when noise is a fractional Brownian motion with Hurst parameter H \in [1/2,1).
This paper deals with the problem of global parameter estimation of affine diffusions in $\mathbb{R}_+ \times \mathbb{R}^n$ denoted by $AD(1, n)$ where $n$ is a positive integer which is a subclass of affine diffusions introduced by Duffie et al in [14]. The $AD(1, n)$ model can be applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models. Our first result is about the classification of $AD(1, n)$ processes according to the subcritical, critical and supercritical cases. Then, we give the stationarity and the ergodicity theorems…
We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.
Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $σ>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we propose a consistent estimator of the parameter $θ=(H,σ)$ combining the ideas of a quasi-likelihood function based on a local Gaussian approximation of a high-frequently observed time series and its frequency-domain approximation. Moreover, we prove an asymptotic normality property of the proposed estimator for all $H\in(0,1)$ when the drift process is constant.
This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from \cite{CK19}
We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we obtain the asymptotic normality and moment convergence of maximum likelihood estimator of the drift parameter .
We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter $H<1/2$ and the mean of its stationary distribution is not equal to zero. In this paper, we derive asymptotically efficient rates and variances of estimators of drift parameters and prove an asymptotic efficiency of a maximum likelihood estimator of drift parameters.
Maximum likelihood, neural networks and posterior mean for inferring fractional Brownian motion parameters
School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）；School of Mathematical Sciences, Queensland University of Technology (QUT)（昆士兰科技大学数理科学学院）；ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems, QUT（昆士兰科技大学ARC细胞系统数学分析卓越中心）
Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift
生物流体的体积限制和低产量阈值已经导致被动微粒流变学的广泛使用。焊珠位置时间序列（焊珠路径）的均方位移（MSD）统计数据可直接用于确定蠕变柔量[Xu et al（1998）]，也可转换用于确定动态储能和损耗模量[Mason & Weitz（1995）]。一个普遍的障碍出现时，有一个非扩散的实验数据漂移。与相对于扩散迁移率的漂移幅度（由Péclet数量化）相一致，MSD统计是失真的，因此必须对路径数据进行漂移“校正”。标准方法是估计并从粒子路径中减去漂移，然后计算MSD统计。我们提出了一种替代的，参数化的方法，使用极大似然估计，同时适合漂移和扩散模型参数的路径数据，MSD统计（因此，遵守和动态模量），然后直接从最佳拟合模型。我们说明和比较这两种方法的模拟路径数据在一个范围内的Péclet数，其中确切的答案是已知的。我们选择分数布朗运动作为数值模型，因为它提供了可调的，亚扩散MSD统计与典型的30秒长，在几种生物流体中的微珠的实验观察一致。最后，我们应用和比较这两种方法的数据从人支气管上皮细胞培养粘液。
