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We establish a moderate deviation principle for the maximum likelihood estimator of the four parameters of a geometrically ergodic Heston process. We also obtain moderate deviations for the maximum likelihood estimator of the couple of…

Probability · Mathematics 2018-01-26 Marie du Roy de Chaumaray

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…

Statistics Theory · Mathematics 2021-01-19 Chunhao Cai , Min Zhang

We examine a mean-reverting Ornstein-Uhlenbeck process that perturbs an unknown Lipschitz-continuous drift and aim to estimate the drift's value at a predetermined time horizon by sampling the path of the process. Due to the time varying…

Statistics Theory · Mathematics 2024-05-20 Enrico Bernardi , Alberto Lanconelli , Christopher S. A. Lauria , Berk Tan Perçin

We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary…

Probability · Mathematics 2016-04-12 Alexander Kukush , Yuliya Mishura , Kostiantyn Ralchenko

We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter $H<1/2$. Our methods are based on an equidistant discretization of the…

Probability · Mathematics 2016-06-14 Andreas Neuenkirch , Taras Shalaiko

In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general…

Statistics Theory · Mathematics 2025-10-09 Chiara Amorino , Francisco Pina , Mark Podolskij

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Statistics Theory · Mathematics 2024-03-12 Sara Mazzonetto , Paolo Pigato

Piecewise $\alpha$-stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Euler-Maruyama (EM) scheme more difficult to analyze. We…

Probability · Mathematics 2024-11-11 Xinghu Jin , Guodong Pang , Yu Wang , Lihu Xu

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

Statistics Theory · Mathematics 2018-08-21 Miljenko Huzak

We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…

Statistics Theory · Mathematics 2019-04-03 Shogo H. Nakakita , Masayuki Uchida

We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.

Probability · Mathematics 2016-07-14 Dmytro Marushkevych

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…

Analysis of PDEs · Mathematics 2020-01-22 Davit Martirosyan , Vahagn Nersesyan

We consider a continuous time process that is self-exciting and ergodic, called threshold Chan-Karolyi-Longstaff-Sanders (CKLS) process. This process is a generalization of various models in econometrics, such as Vasicek model,…

Statistics Theory · Mathematics 2025-04-15 Sara Mazzonetto , Benoît Nieto

We establish large deviation principles for the couple of the maximum likelihood estimators of dimensional and drift coefficients in the generalised squared radial Ornstein-Uhlenbeck process. We focus our attention to the most tractable…

Probability · Mathematics 2016-11-28 Marie du Roy de Chaumaray

Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…

Statistical Finance · Quantitative Finance 2026-05-19 Ranieri Dugo , Giacomo Giorgio , Paolo Pigato

We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.

Probability · Mathematics 2012-12-13 Bernard Bercu , Frederic Proia , Nicolas Savy

This paper establishes the quantitative stability of invariant measures $\mu_{\alpha}$ for $\mathbb{R}^d$-valued ergodic stochastic differential equations driven by rotationally invariant multiplicative $\alpha$-stable processes with…

Probability · Mathematics 2025-09-17 Xinghu Jin , Xiaolong Zhang

Our goal is to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck process without tears. We propose a new strategy to establish large deviation…

Statistics Theory · Mathematics 2016-02-09 Bernard Bercu , Adrien Richou

We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node.…

Methodology · Statistics 2022-07-12 Valentin Courgeau , Almut E. D. Veraart

In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…

Statistics Theory · Mathematics 2017-12-15 Héctor Araya , Natalia Bahamonde , Tania Roa , Soledad Torres