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 |
|---|---|
| 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 |
Keywords
- Branching process
- Brownian motion
- Exponential growth
- Gaugeability
- Principal eigenvalue
- Schrödinger operator
- Symmetric α-stable process
ASJC Scopus subject areas
- Mathematics(all)