A U-statistic of a Poisson point process is defined as the sum ∑ f (x₁, · · ·, xk) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, ...

This is a preview. Log in through your library . Abstract Consider a renewal process. The renewal events partition the process into i.i.d. renewal cycles. Assume that on each cycle, a rare event ...