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Numerical Attractors via Discrete Rough Paths

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Abstract

We study a rough difference equation on a discrete time set, where the driving Hölder rough path is a realization of a stochastic process. Using a modification of Davie’s approach (Cong et al. in J. Dyn. Differ. Equ. 34:605–636, 2022) 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 Duc and Kloeden (Numerical attractors for rough differential equations, 2021) on the existence and upper semi-continuity of a global random pullback attractor under the dissipativity and the linear growth condition for the drift.

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Acknowledgements

This work is supported by the project NVCC01.10/22-23 of Vietnam Academy of Science and Technology. The authors would like also to thank Vietnam Institute for Advanced Study in Mathematics (VIASM) for a three month research stay in 2021–2022.

Funding

Details of any funding received: project NVCC01.10/22-23 of Vietnam Academy of Science and Technology.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Nguyen Dinh Cong & Luu Hoang Duc

  2. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany

    Luu Hoang Duc

  3. Thang Long University, Hanoi, Vietnam

    Phan Thanh Hong

Authors
  1. Nguyen Dinh Cong
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  2. Luu Hoang Duc
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  3. Phan Thanh Hong
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Applicable for submissions with multiple authors): the authors contribute equally to the manuscript.

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Correspondence to Luu Hoang Duc.

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Cong, N.D., Duc, L.H. & Hong, P.T. Numerical Attractors via Discrete Rough Paths. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10280-4

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  • DOI: https://doi.org/10.1007/s10884-023-10280-4

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