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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Yasuhito Nishimori

摘要

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.