论文标题
具有远距离依赖性和乘法噪声的随机模型的极端的相变
Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise
论文作者
论文摘要
我们考虑一个随机过程，其远程依赖性受到乘法噪声的影响。原始过程和噪声的边际分布都具有定期变化的尾巴，尾部指数$α，α'> 0 $。原始过程被视为定期变化的Karlin模型，这是一个最近研究的模型，其长期依赖性为特征，其特征是（0,1）$中的内存参数$β\。我们为模型的极端建立了限制定理，并揭示了相变。在限制方面，有三种不同的机制：信号义务制度$α<α'β$，噪声占主导地位$α>α'β$和关键方案$α=α'β$。至于证明，我们实际上为所谓的Poisson建立了相同的相变现象，即具有在通用度量空间上定义的乘法噪声的Karlin模型，并采用Poissonization方法来确定一维情况的极限定理。
We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails, with tail indices $α,α'>0$, respectively. The original process is taken as the regularly-varying Karlin model, a recently investigated model that has long-range dependence characterized by a memory parameter $β\in(0,1)$. We establish limit theorems for the extremes of the model, and reveal a phase transition. In terms of the limit there are three different regimes: signal-dominance regime $α<α'β$, noise-dominance regime $α>α'β$, and critical regime $α= α'β$. As for the proof, we actually establish the same phase-transition phenomena for the so-called Poisson--Karlin model with multiplicative noise defined on generic metric spaces, and apply a Poissonization method to establish the limit theorems for the one-dimensional case as a consequence.
