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Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by…

Statistics Theory · Mathematics 2019-04-30 Chen Fei , Weiyin Fei

We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant…

Statistics Theory · Mathematics 2007-12-18 Arnaud Gloter , Marc Hoffmann

We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a change of stability measured with a small parameter $\varepsilon$, we rely on the natural…

Probability · Mathematics 2021-09-21 Dirk Blömker , Alexandra Neamtu

Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with driving noise $ Y_t^{(1)} := \int^t_0 e^{-s}…

Probability · Mathematics 2013-02-26 Ehsan Azmoodeh , Jose Igor Morlanes

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…

Statistics Theory · Mathematics 2022-04-12 Kohei Chiba , Tetsuya Takabatake

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…

Statistics Theory · Mathematics 2020-09-25 Xingzhi Pei

This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…

Methodology · Statistics 2026-01-01 Brijesh Kumar Jha , Subhra Sankar Dhar , Akash Ashirbad Panda

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

Statistics Theory · Mathematics 2025-03-31 Shohei Nakajima

We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified…

Statistics Theory · Mathematics 2016-07-25 Matyas Barczy , Gyula Pap , Tamas T. Szabo

This paper provides several statistical estimators for the drift and volatility parameters of an Ornstein-Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at discrete time…

Probability · Mathematics 2017-03-29 Yaozhong Hu , David Nualart , Hongjuan Zhou

In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is…

Statistics Theory · Mathematics 2020-07-16 Fabien Panloup , Samy Tindel , Maylis Varvenne

In the paper we consider the problem of estimating parameters entering the drift of a fractional Ornstein-Uhlenbeck type process in the non-ergodic case, when the underlying stochastic integral is of Young type. We consider the sampling…

Probability · Mathematics 2019-03-20 Radomyra Shevchenko , Jeannette H. C. Woerner

The statistical analysis for equations driven by fractional Gaussian process (fGp) is relatively recent. The development of stochastic calculus with respect to the fGp allowed to study such models. In the present paper we consider the drift…

Probability · Mathematics 2016-09-28 Mohamed El Machkouri , Khalifa Es-Sebaiy , Youssef Ouknine

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of…

Probability · Mathematics 2015-05-19 Kestutis Kubilius , Viktor Skorniakov , Dmitrij Melichov

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed…

Probability · Mathematics 2012-06-28 K. Kubilius , Y. Mishura

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…

Probability · Mathematics 2019-04-08 H. Araya , J. A. León , S. Torres

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…

Numerical Analysis · Mathematics 2022-01-27 Daxin Nie , Jing Sun , Weihua Deng

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…

Statistics Theory · Mathematics 2017-03-17 Yasutaka Shimizu

Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…

Probability · Mathematics 2018-06-21 Josef Janák

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Statistics Theory · Mathematics 2024-11-07 Arnab Ganguly