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Auteurs principaux:	Cao, Qiyong, Gao, Hongjun, Wei, Wei
Format:	Preprint
Publié:	2025
Sujets:	Probability Dynamical Systems
Accès en ligne:	https://arxiv.org/abs/2510.00954
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author	Cao, Qiyong Gao, Hongjun Wei, Wei
author_facet	Cao, Qiyong Gao, Hongjun Wei, Wei
contents	In this paper, we study a class of dissipative stochastic differential equations driven by nonlinear multiplicative fractional Brownian noise with Hurst index $H \in \left(\frac{1}{3},\frac{1}{2})\cup(\frac{1}{2}, 1\right) $. We establish the well-posedness of the associated coupled stochastic differential equations and prove synchronization in the sense of trajectories. Our approach relies on the Doss-Sussmann transformation, which enables us to extend existing results for additive and linear noise to the case of nonlinear multiplicative fractional Brownian noise. The findings provide new insights into the synchronization of dissipative systems under fractional noise perturbations.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_00954
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Synchronization of stochastic dissipative differential equation driven by fractional Brownian motions Cao, Qiyong Gao, Hongjun Wei, Wei Probability Dynamical Systems In this paper, we study a class of dissipative stochastic differential equations driven by nonlinear multiplicative fractional Brownian noise with Hurst index $H \in \left(\frac{1}{3},\frac{1}{2})\cup(\frac{1}{2}, 1\right) $. We establish the well-posedness of the associated coupled stochastic differential equations and prove synchronization in the sense of trajectories. Our approach relies on the Doss-Sussmann transformation, which enables us to extend existing results for additive and linear noise to the case of nonlinear multiplicative fractional Brownian noise. The findings provide new insights into the synchronization of dissipative systems under fractional noise perturbations.
title	Synchronization of stochastic dissipative differential equation driven by fractional Brownian motions
topic	Probability Dynamical Systems
url	https://arxiv.org/abs/2510.00954

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