Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games

2022/01/19 by Carmina Fjellström, Fjellström, Carmina, Kaj Nyström +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Complex Systems and Time Series Analysis #FOS: Mathematics #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2201.07774

openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The fractional heat operator (∂_t-Δ_x)^s and Continuous Time Random Walks (CTRWs) are interesting and sophisticated mathematical models that can describe complex anomalous systems. In this paper, we prove asymptotic mean value representation formulas for functions with respect to (∂_t-Δ_x)^s and we introduce new nonlocal, nonlinear parabolic operators related to a tug-of-war which accounts for waiting times and space-time couplings. These nonlocal, nonlinear parabolic operators and equations can be seen as nonlocal versions of the evolutionary infinity Laplace operator.

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• Properties of Solutions to the Full Fractional Heat Operator Equation

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