Stochastic Heat Equations defined by Fractal Laplacians on Cantor-like Sets

2019/02/06 by Tim Ehnes, Ehnes, Tim
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1902.02175

openalex publication_date 2019/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study stochastic heat equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we first investigate the corresponding heat kernels. Then, we prove existence and uniqueness of mild solutions to stochastic heat equations provided some Lipschitz and linear growth conditions. We establish Hölder continuity in space and time and compute the Hölder exponents. Moreover, we address the question of weak intermittency.

Citations

• One-parameter semigroups for linear evolution equations
• Spectral Asymptotics for Krein-Feller-Operators with respect to \boldsymbol V-Variable Cantor Measures

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