STOCHASTIC PROCESSES ON WEAKLY LOGARITHMIC ASSEMBLIES

We explore the weak convergence of processes defined on random weakly logarithmic combinatorial assemblies as their sizes unboundedly increase. If the limit process has independent non-degenerate increments, we establish necessary and sufficient convergence conditions. The sufficiency part is based upon the total variation approximation for the distribution of component vector by that of a vector with independent coordinates. The proof of necessity essentially exploits the independence of increments.