• Corpus ID: 85517481

# On the tail distribution of the solution to some law equation

@article{Chen2019OnTT,
title={On the tail distribution of the solution to some law equation},
author={Xinxing Chen and Chunhua Ma},
journal={arXiv: Probability},
year={2019}
}
• Published 26 March 2019
• Mathematics
• arXiv: Probability
We consider a distribution equation which was initially studied by Bertoin \cite{Bertoin}: $M \stackrel{d}{=} \max\{\widetilde{\nu}, \max_{1\leq k\leq \nu}M_k\}.$ where $\{M_k\}_{k\geq 1}$ are i.i.d. copies of $M$ and independent of $(\widetilde{\nu}, \nu)\in\mathbb{R}_+\times\mathbb{N}$. We obtain the tail behaviour of the solution of a generalised equation in a different but direct method by considering the joint tail of $(\widetilde{\nu}, \nu)$.
1 Citations

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