Abstract
We consider a critical superprocess {X;Pμ} with general spatial motion and spatially dependent stable branching mechanism with lowest stable index γ0>1. We first show that, under some conditions, Pμ(|Xt|≠0) converges to 0 as t→∞ and is regularly varying with index (γ0−1)−1. Then we show that, for a large class of non-negative testing functions f, the distribution of {Xt(f);Pμ(⋅|‖Xt‖≠0)}, after appropriate rescaling, converges weakly to a positive random variable z(γ0−1) with Laplace transform E[e−uz(γ0−1)]=1−(1+u−(γ0−1))−1∕(γ0−1).
Original language | English (US) |
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Pages (from-to) | 4358-4391 |
Number of pages | 34 |
Journal | Stochastic Processes and their Applications |
Volume | 130 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2020 |
Keywords
- Critical superprocess
- Intrinsic ultracontractivity
- Regular variation
- Scaling limit
- Stable branching
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics