Limit theorems for some critical superprocesses

zbMATH Open1338.60074arXiv1403.1342MaRDI QIDQ5965365

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Publication date: 3 March 2016

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Abstract: In this paper we establish some conditional limit theorems for some critical superprocesses $X=X_t,tge0$. First we identify the rate of non-extinction. Then we show that, for a large class of functions $f$, conditioned on non-extinction at time $t$, the limit, as $toinfty$, of $t^{-1}langlef,X_{t}angle$ exists in distribution and we identify this limit. Finally, we also establish, under some conditions, a central limit theorem for $langlef,X_{t}angle$ conditioned on non-extinction at time $t$.

Full work available at URL: https://arxiv.org/abs/1403.1342

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