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MiS Preprint

Numerical attractors via discrete rough paths

Dinh Cong Nguyen, Hoang Duc Luu and Thanh Hong Phan


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.

Apr 6, 2023
Apr 6, 2023

Related publications

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)