Survival probability for jump processes in unbounded domains on metric measure spaces
Abstract
We study the large time behavior of the survival probability PxτD>t for symmetric jump processes in unbounded domains with a positive bottom of the spectrum. We prove asymptotic upper and lower bounds with explicit constants in terms of the bottom of the spectrum λ(D). Our main result applies to symmetric jump processes in general metric measure spaces. For α-stable processes in unbounded uniformly C1,1 domains, our results provide a probabilistic interpretation and an equivalent geometric condition for λ(D)>0. In the case of increasing horn-shaped domains, the exponential rate of decay for the survival probability is sharp. We also present examples of unbounded domains where our results apply.
Fields of Study & Subjects
Stochastic processes and financial applications
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–24
- Publication date
- 1 January 2026
- Language
- EN