Stochastic coalescence with homogeneous-like interaction rates

We study infinite systems of particles characterized by their masses. Each pair of particles with masses xx and yy coalesces at a given rate K(x,y)K(x,y). We consider, for each λ∈Rλ∈R, a class of homogeneous (or homogeneous-like) coagulation kernels KK. We show that such processes exist as strong Markov–Feller processes with values in ℓλℓλ, the set of ordered [0,∞][0,∞]-valued sequences (mi)i≥1(mi)i≥1 such that ∑i≥1miλ<∞.