论文标题
渐近平均价值公式，非本地时空抛物线运算符和异常拔河游戏
Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games
论文作者
论文摘要
分数热运算符$（\ partial_t-δ_x）^s $和连续的时间随机步行（CTRWS）是有趣且复杂的数学模型，可以描述复杂的异常系统。在本文中，我们证明了有关$（\ partial_t-Δ_x）^s $函数的渐近平均值表示公式，并且我们引入了与拖拉机的拖拉机和时空耦合有关的新型非局部非线性非线性抛物线运算符。这些非本地的非线性抛物线算子和方程式可以看作是进化无限拉普拉斯算子的非本地版本。
The fractional heat operator $(\partial_t-Δ_x)^s$ 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 $(\partial_t-Δ_x)^s$ 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.
