发表机构
Wrocław University of Science and Technology; Union College; Saint Louis University; Purdue University（弗罗茨瓦夫科技大学; 联合学院; 圣路易斯大学; 普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究无界开集上对称Lévy过程的Feynman-Kac半群的大时间渐近，证明生存概率的精确指数衰减率由非局部薛定谔算子谱下确界给出，并建立谱性质与生存概率衰减的直接联系。
AI 中文摘要
我们研究了无界开集上对称Lévy过程的Feynman-Kac半群的大时间渐近行为。我们的主要结果证明了生存概率的精确指数渐近衰减率，该衰减率由相关非局部薛定谔算子谱的下确界给出。我们还证明了带有显式多项式修正的定量上界。证明是概率性的，通过将Lévy过程分解为一个收集小跳跃的有限范围跳跃过程和一个描述大跳跃的独立复合泊松过程来完成。我们的方法在非局部薛定谔算子的谱性质与生存概率的逐点衰减之间建立了直接联系，这一联系此前对于跳跃过程是未知的。
英文摘要
We study the large time asymptotics of the Feynman-Kac semigroups of the symmetric Lévy process on unbounded open sets. Our main result proves the exact exponential asymptotic decay rate for the survival probability given in terms of the bottom of the spectrum of the associated nonlocal Schrödinger operator. We also prove quantitative upper bounds with an explicit polynomial correction. The proof is probabilistic and is done by decomposing the Lévy process into a finite-range jump process collecting the small jumps and an independent compound Poisson process describing the large jumps. Our approach gives a direct link between the spectral properties of nonlocal Schrödinger operators and pointwise decay of survival probabilities, which was previously unknown for jump processes.
Comments22 pages, 2 figures
