Large time behavior of Lévy processes and their nonlocal Schrödinger semigroups
Mateusz Kwaśnicki, Phanuel Mariano, Hugo Panzo, Jing Wang
Source abstract
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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.