Journal of the Mathematical Society of Japan

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


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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.

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

First available in Project Euclid: 24 March 2008

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Zentralblatt MATH identifier

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

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


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.

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