### 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.

Original language | English |
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Pages (from-to) | 75-116 |

Number of pages | 42 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2008 |

Externally published | Yes |

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### Keywords

- Branching process
- Brownian motion
- Exponential growth
- Gaugeability
- Principal eigenvalue
- Schrödinger operator
- Symmetric α-stable process

### ASJC Scopus subject areas

- Mathematics(all)