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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Numerical attractors via discrete rough paths
Dinh Cong Nguyen, Hoang Duc Luu and Thanh Hong PhanAbstract
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:
- 06.04.23
- Published:
- 06.04.23