We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space D[0,∞) under the J1 or M1 topology. The limiting...

The Bernoulli sieve is the infinite “balls-in-boxes” occupancy scheme with random frequencies Pk=W1⋯Wk−1(1−Wk), where (Wk)k∈N are independent copies of a random variable W taking values in (0,1). Assuming that the number of balls equals n, let Ln denote the number of empty boxes...