Abstract
We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.
| Original language | English |
|---|---|
| Pages (from-to) | 1077-1090 |
| Number of pages | 14 |
| Journal | Journal of Applied Probability |
| Volume | 43 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 1 2006 |
Keywords
- Branching process
- Brownian motion
- Extinction
- Gaugeability
- Local extinction
- Principal eigenvalue
- Symmetric α-stable process
- Time change
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty
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Shiozawa, Y. (2006). Extinction of branching symmetric α-stable processes. Journal of Applied Probability, 43(4), 1077-1090. https://doi.org/10.1239/jap/1165505209