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Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses |
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| Authors: | Ren Yan-Xia Song Renming Sun Zhenyao |
| Institution: | 1.School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China ;2.Center for Statistical Science, Peking University, Beijing, 100871, P.R. China ;3.Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA ; |
| 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. |
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