Abstract
We investigate the evolution of particles near the frontier and determine the limiting distribution of these particles, for the branching symmetric α-stable processes. Here, we assume that the branching rate measure is the compactly supported Kato class measure. This process is characterized by the Schrödinger-type operator. Then, these asymptotic properties are determined by the characteristic quantities such as the eigenvalue and eigenfunction of it. By using these, we prove limit theorems. This research is an extension of Nishimori [Limiting distributions for particles near the frontier of spatially inhomogeneous branching Brownian motions. Acta Appl. Math. 184(10) (2023)] on the branching Brownian motions.
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