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An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi-parameter Young fields

Stochastics and Partial Differential Equations: Analysis and Computations volume 9, pages 746–788 (2021)Cite this article

Abstract

This article extends the celebrated Sewing lemma, known from the theory of rough paths, to multi-parameter fields on hyper-cubes. We use this to construct Young integrals for multi-parameter Hölder fields on general domains \(\left[ 0,T\right] ^{k}\) with \(k\ge 1\) taking values in \({\mathbb {R}}^{d}\). Moreover, we show existence, uniqueness and stability of some particular types of hyperbolic SPDEs driven by space-time Hölder noise in a Young regime.

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Acknowledgements

The author is grateful for all the assistance, comments and advice received from Professor Frank N. Proske during the work on this project. Furthermore, we thank Professor Fred E. Benth and Professor Samy Tindel, for great discussions and comments on this project. At last we would like to thank the anonymous referee, whose detailed report with comments and suggestions is highly appreciated, and has helped improve the article to its current form.

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  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Fabian A. Harang

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  1. Fabian A. Harang
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Correspondence to Fabian A. Harang.

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Harang, F.A. An extension of the sewing lemma to hyper-cubes and hyperbolic equations driven by multi-parameter Young fields. Stoch PDE: Anal Comp 9, 746–788 (2021). https://doi.org/10.1007/s40072-020-00184-5

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  • DOI: https://doi.org/10.1007/s40072-020-00184-5

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