Global Dirichlet Heat Kernel Estimates for Symmetric Lévy Processes in Half-Space

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• 作者：Zhen-Qing Chen ; Panki Kim
• 关键词：Dirichlet heat kernel ; Transition density ; Survival probability ; Exit time ; Lévy system ; Lévy process ; Symmetric Lévy process
• 刊名：Acta Applicandae Mathematicae
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：146
• 期：1
• 页码：113-143
• 全文大小：1,015 KB
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036
• 卷排序：146

文摘

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) Lévy processes on half spaces for all \(t>0\). These Lévy processes may or may not have Gaussian component. When Lévy density is comparable to a decreasing function with damping exponent \(\beta\), our estimate is explicit in terms of the distance to the boundary, the Lévy exponent and the damping exponent \(\beta\) of Lévy density.