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MiS Preprint
4/2023

Numerical attractors via discrete rough paths

Dinh Cong Nguyen, Hoang Duc Luu and Thanh Hong Phan

Abstract

We study a rough difference equation on a discrete time set, where the driving Hoelder rough path is a realization of a stochastic process. Using a modification of Davie's approach [6] and the discrete sewing lemma, we derive norm estimates for the discrete solution. In particular, when the discrete time set is regular, the system generates a discrete random dynamical system. We also generalize a recent result in [10] on the existence and upper semi-continuity of a global random pullback attractor under the dissipativity and the linear growth condition for the drift.

Received:
Apr 6, 2023
Published:
Apr 6, 2023

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inJournal
2023 Repository Open Access
Dinh Truong Nguyen, Hoang Duc Luu and Phan Thanh Hong

Numerical attractors via discrete rough paths

In: Journal of dynamics and differential equations, (2023)