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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 first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…

Probability · Mathematics 2011-03-18 Shuai Jing

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 apply the averaging method to a coupled system consisting of two evolution equations which has a slow component driven by fractional Brownian motion (FBM) with the Hurst parameter $H_1> \frac12$ and a fast component driven by additive…

Probability · Mathematics 2023-06-06 Bin Pei , Bjoern Schmalfuss , Yong Xu

In this paper, we establish the propagation of chaos and Euler-Maruyama method of DDSDE driven by multiplicative fractional Brownian motion with Hurst parameter $H\in (\frac{\sqrt{5}-1}{2},1)$. We have not only obtained an upper bound for…

Probability · Mathematics 2025-12-22 Guangjun Shen , Jiangpeng Wang , Xuekang Zhang

In this note we prove the existence of a density for the law of the solution for 1-dimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H…

Probability · Mathematics 2023-02-09 Mireia Besalú , David Márquez-Carreras , Carles Rovira

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

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…

Numerical Analysis · Mathematics 2020-11-18 Jean Daniel Mukam , Antoine Tambue

This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the…

Numerical Analysis · Mathematics 2023-02-21 Xinjie Dai , Jialin Hong , Derui Sheng , Tau Zhou

In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904,…

Computational Finance · Quantitative Finance 2021-12-16 Christian Bayer , Eric Joseph Hall , Raúl Tempone

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

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…

Numerical Analysis · Mathematics 2020-10-02 Charles-Edouard Bréhier

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a…

Probability · Mathematics 2022-01-27 João Guerra , David Nualart

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show that there is a unique solution, which has…

Probability · Mathematics 2007-11-19 Yaozhong Hu , David Nualart , Xiaoming Song

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

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and…

Probability · Mathematics 2008-04-03 Igor Cialenco , Sergey Lototsky , Jan Pospisil

In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…

Probability · Mathematics 2026-01-12 Amjad Saef , Wilhelm Stannat

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

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

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