Limit theorems for branching Markov processes

Zhen Qing Chen, Yuichi Shiozawa

    Research output: Contribution to journalArticlepeer-review

    24 Citations (Scopus)

    Abstract

    We establish almost sure limit theorems for a branching symmetric Hunt process in terms of the principal eigenvalue and the ground state of an associated Schrödinger operator. Here the branching rate and the branching mechanism can be state-dependent. In particular, the branching rate can be a measure belonging to a certain Kato class and is allowed to be singular with respect to the symmetrizing measure for the underlying Hunt process X. The almost sure limit theorems are established under the assumption that the associated Schrödinger operator of X has a spectral gap. Such an assumption is satisfied if the underlying process X is a Brownian motion, a symmetric α-stable-like process on Rn or a relativistic symmetric stable process on Rn.

    Original languageEnglish
    Pages (from-to)374-399
    Number of pages26
    JournalJournal of Functional Analysis
    Volume250
    Issue number2
    DOIs
    Publication statusPublished - Sept 15 2007

    Keywords

    • Branching Markov processes
    • Dirichlet form
    • Gaugeability
    • Limit theorem
    • Schrödinger operator
    • h-Transform

    ASJC Scopus subject areas

    • Analysis

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