An almost sure scaling limit theorem for Dawson–Watanabe superprocesses
An almost sure scaling limit theorem for Dawson–Watanabe superprocesses
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DOI：
10.1016/j.jfa.2007.12.003
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发表时间：
2008-04
影响因子：
1.7
通讯作者：
Zhen-Qing Chen;Yanxia Ren;Hao Wang
中科院分区：
文献类型：
--
作者：
Zhen-Qing Chen;Yanxia Ren;Hao Wang
建立了一大类空间运动为对称Hunt过程的Dawson-Watanabe超过程的标度极限定理，其中收敛在概率意义下收敛。当下标过程是具有Cb1-系数的对称扩散过程，或者是R上的对称Lévy过程，其Lévy指数Ψ(η)对某个c>；0和α∈(0，2)自下有界时，当|η|较大时，建立了该超过程的一个更强的几乎必然极限定理.我们的方法使用了一些相关薛定谔算子的主本征值和基态。极限定理是在假设相关联的薛定谔算子具有谱间隙的情况下建立的。
We establish a scaling limit theorem for a large class of Dawson–Watanabe superprocesses whose underlying spatial motions are symmetric Hunt processes, where the convergence is in the sense of convergence in probability. When the underling process is a symmetric diffusion with Cb1-coefficients or a symmetric Lévy process on Rdwhose Lévy exponent Ψ(η) is bounded from below by c|η|αfor some c>0 and α∈(0,2) when |η| is large, a stronger almost sure limit theorem is established for the superprocess. Our approach uses the principal eigenvalue and the ground state for some associated Schrödinger operator. The limit theorems are established under the assumption that an associated Schrödinger operator has a spectral gap.