Spatial Central Limit Theorem for Supercritical Superprocesses
| Autor: | Piotr Miłoś |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Normalization (statistics) Mathematics(all) General Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences 010104 statistics & probability symbols.namesake Poincaré conjecture symbols Infinitesimal generator Limit (mathematics) 0101 mathematics Statistics Probability and Uncertainty Diffusion (business) Smoothing Mathematical physics Central limit theorem Mathematics Superprocess |
| Zdroj: | Journal of Theoretical Probability. 31:1-40 |
| ISSN: | 1572-9230 0894-9840 |
| DOI: | 10.1007/s10959-016-0704-6 |
| Popis: | We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple \((L,\psi )\), where L is the infinitesimal generator of a strongly recurrent diffusion in \(\mathbb {R}^{d}\) and \(\psi \) is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincare 42(2):171–185, 2006), to fulfill a law of large numbers for the spatial distribution of the mass. In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition” of the local growth induced by branching and global smoothing due to the strong recurrence of L. We also prove that the spatial fluctuations are asymptotically independent of the fluctuations of the total mass of the process. |
| Databáze: | OpenAIRE |
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