Growth-fragmentation process embedded in a planar Brownian excursion

Abstract

The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane $${\mathbb {H}}$$ , obtained by cutting the excursion at horizontal levels. We prove that the associated growth-fragmentation is related to one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski in (Bertoin et al. Probab Theory Relat Field 172:663–724, 2018).