Journal of the Mathematical Society of Japan

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

Yuichi SHIOZAWA

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 1 (2008), 75-116.

Dates
First available in Project Euclid: 24 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1206367956

Digital Object Identifier
doi:10.2969/jmsj/06010075

Mathematical Reviews number (MathSciNet)
MR2392004

Zentralblatt MATH identifier
1134.60054

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G52: Stable processes 60J55: Local time and additive functionals

Keywords
branching process Brownian motion symmetric $\alpha$-stable process exponential growth Schrödinger operator principal eigenvalue gaugeability

Citation

SHIOZAWA, Yuichi. Exponential growth of the numbers of particles for branching symmetric $\alpha$ -stable processes. J. Math. Soc. Japan 60 (2008), no. 1, 75--116. doi:10.2969/jmsj/06010075. https://projecteuclid.org/euclid.jmsj/1206367956


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