Occupation Time Fluctuations of Weakly Degenerate Branching Systems
Occupation Time Fluctuations of Weakly Degenerate Branching Systems
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DOI：
10.1007/s10959-011-0358-3
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发表时间：
2011-04
影响因子：
0.8
通讯作者：
Yuqiang Li;Yimin Xiao
中科院分区：
文献类型：
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作者：
Yuqiang Li;Yimin Xiao
建立了具有各向异性空间运动和弱简并分裂能力的一系列分支粒子系统的重标化占用时间涨落的极限定理。在大维度的情况下，我们的极限过程导致了一类新的具有非平稳增量的算子尺度高斯随机场。在中间和临界维中，极限过程具有与Bojdecki等人认为的无退化的临界分支粒子系统所产生的空间结构类似（但比这些结构更复杂）。的过程。应用116:1-18和19-35,2006)。由于弱退化分支能力，这三种情况下的极限过程的时间结构与Bojdecki等人得到的结果不同。的过程。应用116:1-18和19-35,2006)。
We establish limit theorems for rescaled occupation time fluctuations of a sequence of branching particle systems in ℝdwith anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit processes lead to a new class of operator-scaling Gaussian random fields with nonstationary increments. In the intermediate and critical dimensions, the limit processes have spatial structures analogous to (but more complicated than) those arising from the critical branching particle system without degeneration considered by Bojdecki et al. (Stoch. Process. Appl. 116:1–18 and 19–35, 2006). Due to the weakly degenerate branching ability, temporal structures of the limit processes in all three cases are different from those obtained by Bojdecki et al. (Stoch. Process. Appl. 116:1–18 and 19–35, 2006).