Abstract
In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.
Original language | English (US) |
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Pages (from-to) | 91-131 |
Number of pages | 41 |
Journal | Acta Applicandae Mathematicae |
Volume | 165 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 2020 |
Keywords
- 2-Spine decomposition
- Asymptotic behavior of the survival probability
- Critical superprocess
- Martingale change of measure
- Size-biased Poisson random measure
- Spine decomposition
- Yaglom’s exponential limit law
ASJC Scopus subject areas
- Applied Mathematics