稳定网的构建和收敛结果

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-06-19 DOI:10.1016/j.spa.2024.104415

Thomas Mountford , Krishnamurthi Ravishankar

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引用次数: 0

摘要

我们为老化路径集合引入了一种新的度量，并引入了一系列稳健的条件，这些条件意味着在与该度量相对应的拓扑中老化路径集合的紧凑性。我们证明，由稳定路径集合组成的稳定网（1<α≤2）的分布在此拓扑中是紧密的。然后，我们展示了随机漫步（适当归一化）凝聚系统向稳定网的收敛。我们还得到了布朗情况下的一些路径结果。

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Construction and convergence results for stable webs

We introduce a new metric for collections of aged paths and a robust set of conditions implying compactness for set of collections of aged paths in the topology corresponding to this metric. We show that the distribution of stable webs ( $1 < α \leq 2$ ) made up of collections of stable paths is tight in this topology. We then show convergence to stable webs for coalescing systems of random walks(suitably normalized). We obtain some path results in the Brownian case.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.