Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

  • Yan-Xia Ren
  • Renming Song
  • Zhenyao SunEmail author


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.


Critical superprocess Size-biased Poisson random measure Spine decomposition 2-Spine decomposition Asymptotic behavior of the survival probability Yaglom’s exponential limit law Martingale change of measure 

Mathematics Subject Classification (2010)

60J80 60F05 



We thank the two referees for very helpful comments on the first version of this paper.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingP.R. China
  2. 2.Center for Statistical SciencePeking UniversityBeijingP.R. China
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  4. 4.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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