Limit Theorems for the Rightmost Particle in the Locally Inhomogeneous Branching Brownian Motion

Yasuhito Nishimori ()
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Yasuhito Nishimori: National Institute of Technology, Anan College

Journal of Theoretical Probability, 2025, vol. 38, issue 2, 1-77

Abstract: Abstract We investigate the evolution of the rightmost particle for the locally inhomogeneous branching Brownian motion. The branching rate measure is the compactly supported Kato class measure. This process is characterized by the Schrödinger-type operator. The asymptotic properties are determined by the characteristic quantities such as the eigenvalue and eigenfunction of it. By using these, we give limit theorems.

Keywords: Branching Brownian motion; Rightmost; Fluctuation; Ergodicity; Feynman–Kac functional; 60J80; 60F15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01402-3

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