## Journal of the Mathematical Society of Japan

### Exponential growth of the numbers of particles for branching symmetric $\alpha$-stable processes

Yuichi SHIOZAWA

#### Abstract

We study the exponential growth of the numbers of particles for a branching symmetric $\alpha$-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

https://projecteuclid.org/euclid.jmsj/1206367956

Digital Object Identifier
doi:10.2969/jmsj/06010075

Mathematical Reviews number (MathSciNet)
MR2392004

Zentralblatt MATH identifier
1134.60054

#### 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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