Numerical attractors via discrete rough paths

Dinh Cong Nguyen, Hoang Duc Luu, and Thanh Hong Phan

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Submission date: 06. Apr. 2023 (revised version: June 2023)
Pages: 24
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DOI number (of the published article): 10.1007/s10884-023-10280-4

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.