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A note on vague convergence of measures

Author

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  • Basrak, Bojan
  • Planinić, Hrvoje

Abstract

We propose a new approach to vague convergence of measures based on the general theory of boundedness due to Hu (1966). The article explains how this connects and unifies several frequently used types of vague convergence from the literature. Such an approach allows one to translate already developed results from one type of vague convergence to another. We further analyze the corresponding notion of vague topology and give a new and useful characterization of convergence in distribution of random measures in this topology.

Suggested Citation

  • Basrak, Bojan & Planinić, Hrvoje, 2019. "A note on vague convergence of measures," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 180-186.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:180-186
    DOI: 10.1016/j.spl.2019.06.004
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    Cited by:

    1. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "Aggregating heavy-tailed random vectors: from finite sums to L\'evy processes," Papers 2301.10423, arXiv.org.
    2. Qian Hui & Tiandong Wang, 2024. "Mitigating Extremal Risks: A Network-Based Portfolio Strategy," Papers 2409.12208, arXiv.org.
    3. Barczy, Mátyás & Basrak, Bojan & Kevei, Péter & Pap, Gyula & Planinić, Hrvoje, 2021. "Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 33-75.

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