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Self-similar stochastic processes with stationary increments as limits of particle systems
Stochastic Analysis and Applications ( IF 0.8 ) Pub Date : 2020-11-23 , DOI: 10.1080/07362994.2020.1844021 Łukasz Treszczotko 1
中文翻译:
以平稳增量作为粒子系统极限的自相似随机过程
更新日期:2020-11-23
Stochastic Analysis and Applications ( IF 0.8 ) Pub Date : 2020-11-23 , DOI: 10.1080/07362994.2020.1844021 Łukasz Treszczotko 1
Affiliation
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:
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。