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Long-time behavior of stochastic evolution equations with multiplicative rough noise

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Seitz_2-1ufr4kqxtyqhm4.pdf
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2025

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http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1ufr4kqxtyqhm4
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Zusammenfassung

This thesis primarily investigates stochastic evolution equations with nonlinear multiplicative noise and their long-term behavior. Due to the stochastic influence, the solutions are, in general, not pathwise defined, which causes several problems when examining long-term behavior. In particular, it is challenging to consider equations with nonlinear multiplicative noise. For this reason, the focus of this work is on pathwise solution concepts. To be more precise, we consider mild solutions using the theory of rough paths and pathwise mild solutions. The results are applied to several examples, such as equations with noise on the boundary. We also highlight some open questions or potential areas for extension.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

rough partial differential equations, mild Gronwall lemma, Lyapunov exponents, rough boundary noise, singular Gronwall inequality, random pullback, stochastic partial differential equations, controlled rough paths, extrapolation operators, Neumann boundary noise., pathwise mild solutions, random dynamical systems, non-autonomuous rough partial differential equations

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ISO 690SEITZ, Tim, 2025. Long-time behavior of stochastic evolution equations with multiplicative rough noise [Dissertation]. Konstanz: Universität Konstanz
BibTex
@phdthesis{Seitz2025Longt-75200,
  title={Long-time behavior of stochastic evolution equations with multiplicative rough noise},
  year={2025},
  author={Seitz, Tim},
  address={Konstanz},
  school={Universität Konstanz}
}
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URL der Originalveröffentl.

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Prüfungsdatum der Dissertation

October 9, 2025
Hochschulschriftenvermerk
Konstanz, Univ., Diss., 2025
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