On Moments of Multiplicative Coalescents

2021/08/26 by Konarovskyi, Vitalii, Limic, Vlada
#05C80 #60G51 #60J75 #60J90 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2108.11799

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 l² 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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