Stochastic Coalescence Multi-Fragmentation Processes

Abstract

We study infinite systems of particles which undergo coalescence and fragmentation, in a manner determined solely by their masses. A pair of particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A particle of mass $x$ fragments into a collection of particles of masses $\theta \_1x,\theta \_2x,\dots$ at rate $F(x)\beta (d\theta )$. We assume that the kernels $K$ and $F$ satisfy Hölder regularity conditions with indices $\lambda \in (0,1]$ and $\alpha \in [0,\infty )$ respectively. We show existence of such infinite particle systems as strong Markov processes taking values in $\ell \_\lambda$, the set of ordered sequences $(m\_i)\_i\ge 1$ such that $\sum\_{i \ge 1} m\_i^λ \textless{} \infty$. We show that these processes possess the Feller property. This work relies on the use of a Wasserstein-type distance, which has proved to be particularly well-adapted to coalescence phenomena.

arXiv admin note: substantial text overlap with arXiv:1301.1934

Cited by in corpus (1)

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