Stochastic coalescence multi-fragmentation processes

Eduardo Cepeda

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 360-391

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 θ1x,θ2x,… at rate F(x)β(dθ). We assume that the kernels K and F satisfy Hölder regularity conditions with indices λ∈(0,1] and α∈[0,∞) respectively. We show existence of such infinite particle systems as strong Markov processes taking values in ℓλ, the set of ordered sequences (mi)i≥1 such that ∑i≥1miλ<∞. 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.

Keywords: Stochastic coalescence multi-fragmentation process; Stochastic interacting particle systems (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.09.004

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