Functional Central Limit Theorems for Supercritical Superprocesses
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- Ren, YX., Song, R. & Zhang, R. Acta Appl Math (2017) 147: 137. doi:10.1007/s10440-016-0072-3
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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).