Continuous random field solutions to parabolic SPDEs on p.c.f. fractals

Conference item

We consider a general class of L2-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 H¨older 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.

Authors: Hambly, B; Yang, W

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Springer
• Host title: Stochastic Analysis and Applications 2025: In Honour of Terry Lyons
• Acceptance date: 2025-03-06
• Event title: 2024 Conference on Modern Topics in Stochastic Analysis and Applications (in honour of Terry Lyons’ 70th birthday)
• Event location: Imperial College London, London, UK
• Event website: https://www.imperial.ac.uk/events/168741/conference-on-modern-topics-in-stochastic-analysis-and-applications-in-honour-of-terry-lyons-70th-birthday/
• Event start date: 2024-04-22
• Event end date: 2024-04-26
• Language: English