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We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…

Probability · Mathematics 2019-11-27 Shigeki Aida , Nobuaki Naganuma

We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…

Probability · Mathematics 2025-12-10 Xue-Mei Li , Colin Piernot , Szymon Sobczak , Kexing Ying

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a…

Probability · Mathematics 2012-01-30 Rémi Rhodes , Bamba A. Sow

In this paper, we show that the integration of a stochastic differential equations driven by G-Brownian motion in R can be reduced to the integration of an ordinary differential equations parametrized by a variable in ({\Omega},F). We study…

Probability · Mathematics 2014-09-02 Peng Luo , Falei Wang

The main goal of this article is to derive a two-sided estimate for hitting probabilities of a hypoelliptic stochastic differential equation (SDE) driven by fractional Brownian motion (fBM) with Hurst parameter $H\in(1/4,1)$ in terms of…

Probability · Mathematics 2025-12-09 Xi Geng , Sheng Wang

Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entire flow of its time marginals. We establish the existence and…

Probability · Mathematics 2024-12-17 Zimo Hao , Michael Röckner , Xicheng Zhang

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

In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter H in (1/4; 1/2). Towards this end, we apply Doss-Sussmann representation of the solution and an…

Probability · Mathematics 2019-04-08 H. Araya , J. A. León , S. Torres

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is…

Probability · Mathematics 2011-11-10 Laure Coutin , Peter Friz , Nicolas Victoir

This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…

Probability · Mathematics 2020-12-16 Madalina Deaconu , Samuel Herrmann

We consider upper bounds for the approximation error E|g(X)-g(\hat X)|^p, where X and \hat X are random variables such that \hat X is an approximation of X in the L_p-norm, and the function g belongs to certain function classes, which…

Probability · Mathematics 2007-12-24 Rainer Avikainen

In this paper, we build the equivalence between rough differential equations driven by the lifted $G$-Brownian motion and the corresponding Stratonovich type SDE through the Wong-Zakai approximation. The quasi-surely convergence rate of…

Probability · Mathematics 2020-11-11 Shige Peng , Huilin Zhang

We study strong approximation of scalar additive noise driven stochastic differential equations (SDEs) at time point $1$ in the case that the drift coefficient is bounded and has Sobolev regularity $s\in(0,1)$. Recently, it has been shown…

Probability · Mathematics 2024-03-14 Simon Ellinger , Thomas Müller-Gronbach , Larisa Yaroslavtseva

In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way, following the approach of Gubinelli, we…

Probability · Mathematics 2013-10-24 Andreas Neuenkirch , Ivan Nourdin , Andreas Rößler , Samy Tindel

Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…

Probability · Mathematics 2025-12-25 Yuanping Cui , Xiaoyue Li , Yi Liu , Fengyu Wang

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of…

Probability · Mathematics 2012-06-18 Yuliya Mishura , Georgiy Shevchenko

The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…

Numerical Analysis · Mathematics 2024-09-11 Aurelien Junior Noupelah , Jean Daniel Mukam , Antoine Tambue

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…

Probability · Mathematics 2026-01-12 Saloua Labed , Nacira Agram , Bernt Oksendal

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Computation · Statistics 2012-05-03 Umberto Picchini , Susanne Ditlevsen

In this work, we present a general Milstein-type scheme for McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and Poisson random measure and the associated system of interacting particles where drift,…

Probability · Mathematics 2025-01-08 Sani Biswas , Chaman Kumar , Christoph Reisinger , Verena Schwarz