We use the recently-developed multiparameter theory of additive Lévy processes to establish novel connections between an arbitrary Lévy process in ℝ, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the...

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable....</;>