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Continuous Random Field Solutions to Parabolic SPDEs on P.C.F. Fractals

In: Stochastic Analysis and Applications 2025

Author

Listed:
  • Ben Hambly

    (University of Oxford, Mathematical Institute)

  • Weiye Yang

    (University of Oxford, Mathematical Institute)

Abstract

We consider a general class of $$L^2$$ L 2 -valued stochastic processes that arise primarily as solutions of parabolic SPDEs on post-critically finite fractals. Using a Kolmogorov-type continuity theorem, conditions are found under which these processes admit versions which are function-valued and jointly continuous in space and time, and the associated Hölder exponents are computed. We apply this theorem to the solutions of SPDEs in the theories of both da Prato–Zabczyk and Walsh. We conclude by discussing a version of the parabolic Anderson model on these fractals and demonstrate a weak form of intermittency.

Suggested Citation

  • Ben Hambly & Weiye Yang, 2026. "Continuous Random Field Solutions to Parabolic SPDEs on P.C.F. Fractals," Springer Books, in: Dan Crisan & Ilya Chevyrev & Thomas Cass & James Foster & Christian Litterer & Cristopher Salvi (ed.), Stochastic Analysis and Applications 2025, pages 321-373, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-03914-9_12
    DOI: 10.1007/978-3-032-03914-9_12
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