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arXiv · 1903.10755

On the tail distribution of the solution to some law equation

Xinxin Chen·Chunhua Ma
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Abstract

We consider a distribution equation which was initially studied by Bertoin \cite{Bertoin}: \[M \stackrel{d}{=} \max\{\widetildeν, \max_{1\leq k\leq ν}M_k\}.\] where $\{M_k\}_{k\geq 1}$ are i.i.d. copies of $M$ and independent of $(\widetildeν, ν)\in\mathbb{R}_+\times\mathbb{N}$. We obtain the tail behaviour of the solution of a generalised equation in a different but direct method by considering the joint tail of $(\widetildeν, ν)$.

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Xinxin Chen, Chunhua Ma. 2019-03-26. On the tail distribution of the solution to some law equation. https://arxiv.org/abs/1903.10755

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