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Stochastic coalescence multi-fragmentation processes

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  • Cepeda, Eduardo

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.

Suggested Citation

  • Cepeda, Eduardo, 2016. "Stochastic coalescence multi-fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 360-391.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:2:p:360-391
    DOI: 10.1016/j.spa.2015.09.004
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    References listed on IDEAS

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    1. Cepeda, Eduardo & Fournier, Nicolas, 2011. "Smoluchowski's equation: Rate of convergence of the Marcus-Lushnikov process," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1411-1444, June.
    2. Haas, Bénédicte, 2003. "Loss of mass in deterministic and random fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 245-277, August.
    3. Fournier, Nicolas & Löcherbach, Eva, 2009. "Stochastic coalescence with homogeneous-like interaction rates," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 45-73, January.
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