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In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…

Probability · Mathematics 2007-05-23 Enriquez Nathanael

A well-known result with respect to the one dimensional nearest-neighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the…

Probability · Mathematics 2007-11-02 Magda Peligrad , Sunder Sethuraman

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

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter…

Probability · Mathematics 2012-03-05 Mireia Besalú , Carles Rovira

In this article we investigate the controllability for neutral stochastic functional integro-differential equations with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than $1/2$ in a Hilbert space. We…

Probability · Mathematics 2018-09-26 Brahim Boufoussi , Soufiane Mouchtabih

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

We derive estimates for the solutions to differential equations driven by a H\"older continuous function of order $\beta>1/2$. As an application we deduce the existence of moments for the solutions to stochastic partial differential…

Probability · Mathematics 2007-05-23 Yaozhong Hu David Nualart

Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…

Statistical Mechanics · Physics 2015-11-25 Mathieu Delorme , Kay Joerg Wiese

In this paper we show that under some assumptions, for a $d$-dimensional fractional Brownian motion with Hurst parameter $H>1/2$, the density of solution of stochastic differential equation driven by it has a short-time expansion similar to…

Probability · Mathematics 2010-05-20 Fabrice Baudoin , Cheng Ouyang

The purpose of this paper is to establish the multivariate normal convergence for the average of certain Volterra processes constructed from a fractional Brownian motion with Hurst parameter H>1/2. Some applications to parameter estimation…

Probability · Mathematics 2015-02-12 Ivan Nourdin , David Nualart , Rola Zintout

In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H >…

Probability · Mathematics 2011-04-21 Fabrice Baudoin , Cheng Ouyang , Samy Tindel

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 paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions…

Probability · Mathematics 2023-04-10 Solesne Bourguin , Thanh Dang , Konstantinos Spiliopoulos

In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H.

Probability · Mathematics 2007-05-23 Andreas Neuenkirch , Ivan Nourdin

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…

Probability · Mathematics 2007-05-23 Ivan Nourdin , Ciprian A. Tudor

We study the anticipative backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H greater than 1/2. The stochastic integral used throughout the paper is the divergence…

Probability · Mathematics 2016-11-29 Jiaqiang Wen , Yufeng Shi

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy H\"ormander's condition.…

Probability · Mathematics 2007-05-23 F. Baudoin , M. Hairer

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…

Numerical Analysis · Mathematics 2017-09-18 Guang-an Zou , Guangying Lv , Jiang-Lun Wu

We study a class of mean-field stochastic differential equations driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$ and a related stochastic control problem. We derive a Pontryagin type maximum principle and the…

Optimization and Control · Mathematics 2017-07-10 Rainer Buckdahn , Shuai Jing

We investigate the Local Asymptotic Property for fractional Brownian models based on discrete observations contaminated by a Gaussian moving average process. We consider both situations of low and high-frequency observations in a unified…

Statistics Theory · Mathematics 2023-12-01 Grégoire Szymanski , Tetsuya Takabatake