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- W2875985323 abstract "We consider a critical superprocess ${X;mathbf P_mu}$ with general spatial motion and spatially dependent stable branching mechanism with lowest stable index $gamma_0 > 1$. We first show that, under some conditions, $mathbf P_{mu}(|X_t|neq 0)$ converges to $0$ as $tto infty$ and is regularly varying with index $(gamma_0-1)^{-1}$. Then we show that, for a large class of non-negative testing functions $f$, the distribution of ${X_t(f);mathbf P_mu(cdot||X_t|neq 0)}$, after appropriate rescaling, converges weakly to a positive random variable $mathbf z^{(gamma_0-1)}$ with Laplace transform $E[e^{-umathbf z^{(gamma_0-1)}}]=1-(1+u^{-(gamma_0-1)})^{-1/(gamma_0-1)}.$" @default.
- W2875985323 created "2018-07-19" @default.
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- W2875985323 date "2018-07-08" @default.
- W2875985323 modified "2023-09-24" @default.
- W2875985323 title "Limit theorems for a class of critical superprocesses with stable branching" @default.
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- W2875985323 doi "https://doi.org/10.48550/arxiv.1807.02837" @default.
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