On Moments of Multiplicative Coalescents

Vitalii Konarovskyi; Vlada Limic

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arXiv · 2108.11799

On Moments of Multiplicative Coalescents

Vitalii Konarovskyi·Vlada Limic

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Abstract

We prove existence of all moments of the multiplicative coalescent at all times. We obtain as byproducts a number of related results which could be of general interest. In particular, we show the finiteness of the second moment of the $l^2$ norm for any extremal eternal version of multiplicative coalescent. Our techniques are in part inspired by percolation, and in part are based on tools from stochastic analysis, notably the semi-martingale and the excursion theory.

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Vitalii Konarovskyi, Vlada Limic. 2021-08-26. On Moments of Multiplicative Coalescents. https://arxiv.org/abs/2108.11799

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