Acta Applicandae Mathematicae

, Volume 147, Issue 1, pp 137–175

Functional Central Limit Theorems for Supercritical Superprocesses


DOI: 10.1007/s10440-016-0072-3

Cite this article as:
Ren, YX., Song, R. & Zhang, R. Acta Appl Math (2017) 147: 137. doi:10.1007/s10440-016-0072-3


In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the state \(E\) is a finite set and the underlying motion is an irreducible Markov chain on \(E\), our results are superprocess analogs of the functional central limit theorems of Janson (Stoch. Process. Appl. 110:177–245, 2004) for supercritical multitype branching processes. The results of this paper are refinements of the central limit theorems in Ren et al. (Stoch. Process. Appl. 125:428–457, 2015).


Functional central limit theorem Supercritical superprocess Excursion measures of superprocesses 

Mathematics Subject Classification

60J68 60F05 60G57 60J45 

Funding information

Funder NameGrant NumberFunding Note
Simons Foundation (US)
  • 208236
National Natural Science Foundation of China (CN)
  • 11271030, 11128101

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.LMAM School of Mathematical Sciences & Center for Statistical SciencePeking UniversityBeijingP.R. China
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingP.R. China

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