A central limit theorem for sums of correlated products

摘要

Consider a sequence of random points placed on the nonnegative integers with i.i.d. geometric (1/2) interpoint spacings yi. Let xi denote the numbers of points placed at integer i. We prove a central limit theorem for the partial sums of the sequence x0y0,x1y1, . . . The problem is connected with a question concerning different bootstrap procedures.