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We consider estimation of the drift parameter $\vartheta>0$ in a \emph{partially observed} Ornstein--Uhlenbeck type model driven by a mixed fractional Brownian noise. Our framework extends the partially observed model of…

Statistics Theory · Mathematics 2026-01-12 Chunhao Cai

We investigate the asymptotic properties of maximum likelihood estimators of the drift parameter for fractional vasicek model driven by a sub-fractional Brownian motion.

Probability · Mathematics 2021-06-08 B. L. S. Prakasa Rao

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter $\hat{\cal H} \in ( 1/2, 1)$. Using fixed point techniques, a…

Optimization and Control · Mathematics 2023-01-24 Naima Hakkar , Rajesh Dhayal , Amar Debbouche , Delfim F. M. Torres

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

We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of chaos and mean field convergence to the law of the…

Probability · Mathematics 2025-12-02 Lucio Galeati , Khoa Lê , Avi Mayorcas

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

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

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

Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…

Probability · Mathematics 2025-09-16 Ranieri Dugo , Giacomo Giorgio , Paolo Pigato

In this article, we present the least squares estimator for the drift parameter in a linear regression model driven by the increment of a fractional Brownian motion sampled at random times. For two different random times, Jittered and…

Statistics Theory · Mathematics 2019-02-25 Héctor Araya , Natalia Bahamonde , Lisandro Fermín , Tania Roa , Soledad Torres

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

This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker…

Probability · Mathematics 2024-12-24 Akihiko Takahashi , Toshihiro Yamada

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of…

Probability · Mathematics 2013-08-05 Alexandra Chronopoulou , Samy Tindel

In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a H\"older continuous function with parameter greater that 1/2 via the Young integration setting. Then some…

Probability · Mathematics 2009-12-14 Jorge A. Leon , Samy Tindel

We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…

Probability · Mathematics 2020-02-19 Katharina Eichinger , Christian Kuehn , Alexandra Neamtu

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

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

In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin…

Optimization and Control · Mathematics 2024-12-25 Yuhang Li , Yuecai Han

This paper deals with a Skorokhod's integral based least squares type estimator $\widehat\theta_N$ of the drift parameter $\theta_0$ computed from $N\in\mathbb N^*$ (possibly dependent) copies $X^1,\dots,X^N$ of the solution $X$ of $dX_t…

Statistics Theory · Mathematics 2025-02-25 Nicolas Marie

We present a method for computing parameter sensitivities and response coefficients in Brownian dynamics simulations. The method involves tracking auxiliary variables (Malliavin weights) in addition to the usual particle positions, in an…

Statistical Mechanics · Physics 2012-07-20 Patrick B. Warren , Rosalind J. Allen