2015/08/06 by Eduardo Cepeda, Cepeda, Eduardo
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1508.01499
arXiv admin note: substantial text overlap with arXiv:1301.1934
arxiv created 2015/08/06 · arxiv updated 2015/08/07
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 θ_1 x, θ_2 x, … 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 ℓ_λ, the set of ordered sequences (m_i)_i ≥ 1 such that ∑_i ≥ 1 m_iλ \textless ∞. 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.