Stochastic coalescence with homogeneous-like interaction rates

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