Storage impulsive processes in the merging phase space (Q460556)

Consider two independent sequences of independent random variables identically distributed within each sequence and two independent stationary renewal processes. Define the new sequence of random variables by taking the \(n\)th random variable from the first sequence if the \(n\)th renewal of two merged renewal processes is a renewal in the first one, and the \(n\)th random variable from the second sequence otherwise. The authors consider partial sums of the random variables from the new sequence. They prove a functional weak law of large numbers and a central limit theorem, and study large deviations by means of the asymptotic analysis of an exponential generator.