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 2006 |
| Externally published | Yes |
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Keywords
- Branching process
- Brownian motion
- Extinction
- Gaugeability
- Local extinction
- Principal eigenvalue
- Symmetric α-stable process
- Time change
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
Cite this
Extinction of branching symmetric α-stable processes. / Shiozawa, Yuichi.
In: Journal of Applied Probability, Vol. 43, No. 4, 12.2006, p. 1077-1090.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Extinction of branching symmetric α-stable processes
AU - Shiozawa, Yuichi
PY - 2006/12
Y1 - 2006/12
N2 - 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.
AB - 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.
KW - Branching process
KW - Brownian motion
KW - Extinction
KW - Gaugeability
KW - Local extinction
KW - Principal eigenvalue
KW - Symmetric α-stable process
KW - Time change
UR - http://www.scopus.com/inward/record.url?scp=33947208935&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33947208935&partnerID=8YFLogxK
U2 - 10.1239/jap/1165505209
DO - 10.1239/jap/1165505209
M3 - Article
AN - SCOPUS:33947208935
VL - 43
SP - 1077
EP - 1090
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
IS - 4
ER -