Sufficient conditions in terms of d_h, d_w and Theta are derived for local/global solutions to Wick-renormalized parabolic stochastic quantization equations on rough metric measure spaces, plus invariant measures for the global case.
Continuous random field solutions to parabolic SPDEs on p.c.f. fractals
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abstract
We consider a general class of $L^2$-valued stochastic processes that arise primarily as solutions of parabolic SPDEs on p.c.f. 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.
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2026 1verdicts
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Wick Renormalized Parabolic Stochastic Quantization Equations on Rough Metric Measure Spaces
Sufficient conditions in terms of d_h, d_w and Theta are derived for local/global solutions to Wick-renormalized parabolic stochastic quantization equations on rough metric measure spaces, plus invariant measures for the global case.