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Elementary Pathwise Methods for Nonlinear Parabolic and Transport Type Stochastic Partial Differential Equations with Fractal Noise

In: Modern Stochastics and Applications

Author

Listed:
  • Michael Hinz

    (Bielefeld University)

  • Elena Issoglio

    (King’s College London, Strand)

  • Martina Zähle

    (Friedrich Schiller University, Jena)

Abstract

We survey some of our recent results on existence, uniqueness, and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random situations, they provide corresponding statements for stochastic partial differential equations driven by fractional noises of sufficiently high regularity order. The approach is based on semigroup theory.

Suggested Citation

  • Michael Hinz & Elena Issoglio & Martina Zähle, 2014. "Elementary Pathwise Methods for Nonlinear Parabolic and Transport Type Stochastic Partial Differential Equations with Fractal Noise," Springer Optimization and Its Applications, in: Volodymyr Korolyuk & Nikolaos Limnios & Yuliya Mishura & Lyudmyla Sakhno & Georgiy Shevchenko (ed.), Modern Stochastics and Applications, edition 127, pages 123-141, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-03512-3_8
    DOI: 10.1007/978-3-319-03512-3_8
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    Cited by:

    1. Diego Chamorro & Elena Issoglio, 2022. "Blow‐up regions for a class of fractional evolution equations with smoothed quadratic nonlinearities," Mathematische Nachrichten, Wiley Blackwell, vol. 295(8), pages 1462-1479, August.

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