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We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the…

Numerical Analysis · Mathematics 2020-06-25 Sebastian Riedel , Yue Wu

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Probability · Mathematics 2021-05-26 Xi Chen , Ilya Timofeyev

This paper deals with asymptotic errors, limit theorems for errors between numerical and exact solutions of stochastic differential equation (SDE) driven by one-dimensional fractional Brownian motion (fBm). The Euler-Maruyama, higher-order…

Numerical Analysis · Mathematics 2024-10-01 Kento Ueda

We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the…

Probability · Mathematics 2019-03-07 Jan Gairing , Peter Imkeller , Radomyra Shevchenko , Ciprian A. Tudor

In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this…

Probability · Mathematics 2021-01-11 Chunhao Cai , Qinghua Wang , Weilin Xiao

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

In this paper, we consider the strong convergence order of the exponential integrator for the stochastic heat equation driven by an additive fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. By showing the strong order one…

Numerical Analysis · Mathematics 2020-07-07 Jialin Hong , Chuying Huang

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 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

In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition…

Probability · Mathematics 2007-06-13 Jorge A. Leon , Jaime San Martin

This paper focuses on the numerical scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)\cup (1/2,1)$. The existence and uniqueness of the solutions to…

Numerical Analysis · Mathematics 2024-05-28 Shuaibin Gao , Qian Guo , Zhuoqi Liu , Chenggui Yuan

We consider stochastic flow on n-dimensional Euclidean space driven by fractional Brownian motion with Hurst parameter H greater than half, and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of the ambient…

Probability · Mathematics 2008-08-05 Sreekar Vadlamani

In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have discontinuities in space. Recently it has been shown in…

Probability · Mathematics 2019-04-22 Thomas Müller-Gronbach , Larisa Yaroslavtseva

We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove…

Analysis of PDEs · Mathematics 2009-03-12 Abdelhadi Es--Sarhir , Onno van Gaans , Michael Scheutzow

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 provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…

Probability · Mathematics 2009-11-20 Max-K. von Renesse , Michael Scheutzow

The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…

Numerical Analysis · Mathematics 2026-02-16 Nan Deng , Wanrong Cao

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\textgreater{}1/2$ and multiplicative noise component $\sigma$.…

Probability · Mathematics 2016-01-18 Joaquin Fontbona , Fabien Panloup

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

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of…

Probability · Mathematics 2009-01-20 Istvan Gyöngy , Annie Millet