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We consider a controlled second order differential equation which is partially observed with an additional fractional noise. we study the asymptotic (for large observation time) design problem of the input and give an efficient estimator of…

Probability · Mathematics 2019-04-09 Chunhao Cai , Wujun LV

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of…

Probability · Mathematics 2011-11-10 Andreas Neuenkirch , Samy Tindel

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…

Data Analysis, Statistics and Probability · Physics 2018-05-04 Audun Theodorsen , Odd Erik Garcia , Martin Rypdal

We investigate the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process driven by a Hermite process.

Statistics Theory · Mathematics 2025-11-25 B. L. S. Prakasa Rao

We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear…

Statistics Theory · Mathematics 2022-03-25 Masahiro Kurisaki

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 the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…

Probability · Mathematics 2019-03-07 Radomyra Shevchenko , Ciprian A. Tudor

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…

Probability · Mathematics 2014-03-06 Enrico Bibbona , Susanne Ditlevsen

We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope…

Statistics Theory · Mathematics 2025-10-29 Shogo Nakakita

For an Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter 0<H<1/2, one shows the Berry-Ess\'een bound of the least squares estimator of the drift parameter. Thus, a problem left in the previous paper…

Probability · Mathematics 2019-08-16 Yong Chen , Nenghui Kuang

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

Statistics Theory · Mathematics 2020-09-14 Yaozhong Hu , Yuejuan Xi

We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a Poisson process. In particular, we show that the marginal…

Probability · Mathematics 2025-06-19 Danijel Grahovac , Anastasiia Kovtun , Nikolai N. Leonenko , Andrey Pepelyshev

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

Methodology · Statistics 2024-04-09 Shijie Cui , Xu Guo , Zhe Zhang

We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of…

Probability · Mathematics 2022-11-24 Luigi Amedeo Bianchi , Stefano Bonaccorsi , Luciano Tubaro

We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein-Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with…

Probability · Mathematics 2016-02-19 Marco Dozzi , Yuriy Kozachenko , Yuliya Mishura , Kostiantyn Ralchenko

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…

Statistics Theory · Mathematics 2009-09-29 Boris Buchmann , Ngai Hang Chan

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that…

Probability · Mathematics 2024-08-28 Zhongmin Qian , Xingcheng Xu

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in…

Dynamical Systems · Mathematics 2024-01-17 Tomás Caraballo , Renato Colucci , Javier López-de-la-Cruz , Alain Rapaport

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

Statistics Theory · Mathematics 2022-05-03 Han Yuecai , Zhang Dingwen

Noise aids the encoding of continuous signals into pulse sequences by way of stochastic resonance and endows the encoding device with a preferred frequency. We study encoding by a threshold device based on the Ornstein-Uhlenbeck process,…

Biological Physics · Physics 2007-05-23 Hans E. Plesser , Theo Geisel