Abstract

We give a particle picture interpretation of two recently discovered classes of self-similar stable processes with stationary increments studied by Samorodnitsky et al. and Dombry and Guillotin-Plantard. We study the occupation times of certain Poissonian systems of particles with ±1 charges and i.i.d. heavy-tailed weights, moving independently according to Lévy processes. We also obtain a new class of self-similar stable processes.

中文翻译：

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以平稳增量作为粒子系统极限的自相似随机过程

摘要

我们给出了最近发现的两类自相似稳定过程的粒子图片解释，这些过程由 Samorodnitsky 等人研究。和 Dombry 和 Guillotin-Plantard。我们研究了具有 ±1 电荷和 iid 重尾权重的某些泊松系统的占据时间，根据 Lévy 过程独立移动。我们还获得了一类新的自相似稳定过程。