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We consider a general class of \(L^2\) -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.

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

  • 会议论文

  • 发表日期：

    2026年

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  • Ben Hambly,
  • Weiye Yang

摘要

We consider a general class of \(L^2\) -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.