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 theta(1)x, theta(2)x,... at rate F(x)beta(d theta). We assume that the kernels K and F satisfy Holder regularity conditions with indices lambda is an element of (0, 1] and alpha is an element of [0, infinity) respectively. We show existence of such infinite particle systems as strong Markov processes taking values in l(lambda), the set of ordered sequences (m(i))(i >= 1) such that Sigma(i >= 1) m(i)(lambda) < infinity. 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. (C) 2015 Elsevier B.V. All rights reserved.