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Central limit theorems for supercritical branching Markov processes |
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| Authors: | Yan-Xia Ren Renming Song Rui Zhang |
| Affiliation: | 1. LMAM School of Mathematical Sciences & Center for Statistical Science, Peking University, Beijing, 100871, PR China;2. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA;3. LMAM School of Mathematical Sciences, Peking University, Beijing, 100871, PR China |
| Abstract: | In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1] for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate. |
| Keywords: | Central limit theorem Branching Markov process Supercritical Martingale Eigenfunction expansion |
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