### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Exponential growth of the numbers of particles for branching symmetric α-stable processes.** / Shiozawa, Yuichi.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 60, no. 1, pp. 75-116. https://doi.org/10.2969/jmsj/06010075

}

TY - JOUR

T1 - Exponential growth of the numbers of particles for branching symmetric α-stable processes

AU - Shiozawa, Yuichi

PY - 2008/1

Y1 - 2008/1

N2 - 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.

AB - 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.

KW - Branching process

KW - Brownian motion

KW - Exponential growth

KW - Gaugeability

KW - Principal eigenvalue

KW - Schrödinger operator

KW - Symmetric α-stable process

UR - http://www.scopus.com/inward/record.url?scp=41149157613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41149157613&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06010075

DO - 10.2969/jmsj/06010075

M3 - Article

AN - SCOPUS:41149157613

VL - 60

SP - 75

EP - 116

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -