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We present an innovating sensitivity analysis for stochastic differential equations: We study the sensitivity, when the Hurst parameter~$H$ of the driving fractional Brownian motion tends to the pure Brownian value, of probability…

Probability · Mathematics 2017-02-14 Alexandre Richard , Denis Talay

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…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

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 is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…

Analysis of PDEs · Mathematics 2016-09-09 Hakima Bessaih , María J. Garrido-Atienza , Xiaoying Han , Björn Schmalfuß

In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary integral equation where the integral is defined in…

Probability · Mathematics 2012-03-14 Marco Ferrante , Carles Rovira

Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H \in (1/3, 1/2]$.

Probability · Mathematics 2024-08-27 Francesco C. De Vecchi , Luca M. Giordano , Daniela Morale , Stefania Ugolini

We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hurst parameter $H>\frac{1}{3}$. The system is analyzed using…

Probability · Mathematics 2026-02-10 Eliseo Luongo , Francesco Triggiano

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske

Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral…

Analysis of PDEs · Mathematics 2013-05-06 María J. Garrido-Atienza , Kening Lu , Björn Schmalfuss

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

Sensitivity analysis w.r.t. the long-range/memory noise parameter for probability distributions of functionals of solutions to stochastic differential equations is an important stochastic modeling issue in many applications. In this paper…

Probability · Mathematics 2024-08-30 Alexandre Richard , Denis Talay

We estimate the Hurst parameter $H \in (0,1)$ of a fractional Brownian motion from discrete noisy data, observed along a high frequency sampling scheme. When the intensity $\tau_n$ of the noise is smaller in order than $n^{-H}$ we establish…

Statistics Theory · Mathematics 2022-05-27 Grégoire Szymanski

In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…

Probability · Mathematics 2023-05-25 Yuliya Mishura , Anton Yurchenko-Tytarenko

This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under consideration is possible only if either the length of the…

Statistics Theory · Mathematics 2023-10-09 P. Chigansky , M. Kleptsyna

Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u}d\mu(u), \;\; 0\leq t\leq 1{equation} A different…

Probability · Mathematics 2011-07-20 Mamadou Abdoul Diop , Youssef Ouknine

In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a…

Statistics Theory · Mathematics 2018-07-11 Kohei Chiba

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

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…

Probability · Mathematics 2024-06-27 Fares Alazemi , Abdulaziz Alsenafi , Yong Chen , Hongjuan Zhou

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…

Numerical Analysis · Mathematics 2020-06-08 Yanzhao Cao , Jialin Hong , Zhihui Liu

In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral is a…

Analysis of PDEs · Mathematics 2016-08-10 María J. Garrido-Atienza , Kening Lu , Björn Schmalfuss
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