一维Lévy过程的前沿传播和拟平稳分布
Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
摘要：
我们共同研究了一维Lévy过程的拟平稳分布的存在性和与同一运动相关的Fisher-Kolmogorov-Petrovskiii-Piskunov（F-KPP）方程的行波的存在性.利用S. Harris，我们证明了与中心Lévy过程相关的F-KPP方程的行波的存在性，该过程以速率$r$分支并以速度$c$传播，等效于具有相同运动但漂移的Lévy过程的准稳态分布的存在性由$-c$漂移并在零处消失，平均吸收时间为$1/r$。这也扩展了两种情况下已知的存在条件。正如在一篇配套文章中所讨论的那样，这不仅仅是一个巧合，而是这两种现象之间关系的结果。
英文摘要：
We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate $r$ and travels at velocity $c$ is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by $-c$ and killed at zero, with mean absorption time $1/r$. This also extends the known existence conditions in both contexts. As it is discussed in a companion article, this is not just a coincidence but the consequence of a relation between these two phenomena.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
