Exponential growth of the numbers of particles for branching symmetric α-stable processes

Yuichi Shiozawa

Research output: Contribution to journalArticle

11 Citations (Scopus)


We study the exponential growth of the numbers of particles for a branching symmetric α-stable process in terms of the principal eigenvalue 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 Lebesgue measure. We calculate the principal eigenvalues and give some examples.

Original languageEnglish
Pages (from-to)75-116
Number of pages42
JournalJournal of the Mathematical Society of Japan
Issue number1
Publication statusPublished - Jan 2008
Externally publishedYes



  • Branching process
  • Brownian motion
  • Exponential growth
  • Gaugeability
  • Principal eigenvalue
  • Schrödinger operator
  • Symmetric α-stable process

ASJC Scopus subject areas

  • Mathematics(all)

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