Stochastic coalescence multi-fragmentation processes

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.