Open Access
January, 2008 Exponential growth of the numbers of particles for branching symmetric α -stable processes
J. Math. Soc. Japan 60(1): 75-116 (January, 2008). DOI: 10.2969/jmsj/06010075


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.


Download Citation

Yuichi SHIOZAWA. "Exponential growth of the numbers of particles for branching symmetric α -stable processes." J. Math. Soc. Japan 60 (1) 75 - 116, January, 2008.


Published: January, 2008
First available in Project Euclid: 24 March 2008

zbMATH: 1134.60054
MathSciNet: MR2392004
Digital Object Identifier: 10.2969/jmsj/06010075

Primary: 60J80
Secondary: 60G52 , 60J55

Keywords: branching process , Brownian motion , exponential growth , gaugeability , Principal eigenvalue , ‎Schrödinger operator‎ , Symmetric $\alpha$-stable process

Rights: Copyright © 2008 Mathematical Society of Japan

Vol.60 • No. 1 • January, 2008
Back to Top