多变量重尾 Hawkes 过程簇大小的尾部渐近分析
概率论
2025-04-07 v3
摘要
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution and demonstrate the emergence of a form of multivariate hidden regular variation. Large values of the cluster size vector result from one or several significant jumps. A discrete optimization problem involving any given rare event set of interest determines the exact configuration of these large jumps and the degree of hidden regular variation. Our proofs rely on a detailed probabilistic analysis of the spatiotemporal structure of multiple large jumps in multi-type branching processes.
引用
@article{arxiv.2503.01004,
title = {Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes},
author = {Jose Blanchet and Roger J. A. Laeven and Xingyu Wang and Bert Zwart},
journal= {arXiv preprint arXiv:2503.01004},
year = {2025}
}