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

SHIOZAWA, Yuichi

J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 75-116 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-01-15
Classification: branching process, Brownian motion, symmetric $\alpha$-stable process, exponential growth, Schrödinger operator, principal eigenvalue, gaugeability, 60J80, 60G52, 60J55

@article{1206367956,
     author = {SHIOZAWA, Yuichi},
     title = {Exponential growth of the numbers of particles for branching symmetric $\alpha$ -stable processes},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 75-116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1206367956}
}

SHIOZAWA, Yuichi. Exponential growth of the numbers of particles for branching symmetric $\alpha$ -stable processes. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  75-116. http://gdmltest.u-ga.fr/item/1206367956/