Self-similar signed growth-fragmentations

William Da Silva

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arXiv · 2101.02582

Self-similar signed growth-fragmentations

William Da Silva

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Abstract

Growth-fragmentation processes model the evolution of positive masses which undergo binary divisions. The aim of this paper is twofold. First, we extend the theory of growth-fragmentation processes to allow signed mass. Among others, we introduce genealogical martingales and establish a spinal decomposition for the associated cell system, following arXiv:1605.00581. Then, we study a particular family of such self-similar signed growth-fragmentation processes which arise when cutting half-planar excursions at horizontal levels. When restricting this process to the positive masses, we recover part of the family introduced by Bertoin, Budd, Curien and Kortchemski in arXiv:1605.00581.

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William Da Silva. 2021-01-07. Self-similar signed growth-fragmentations. https://arxiv.org/abs/2101.02582

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