Limit theorems for integral functionals of Hermite-driven processes

摘要

Consider a moving average process X of the form X(t) = integral(t)(-8)phi(t - u) dZ(u), t >= 0, where Z is a (non Gaussian) Hermite process of order q >= 2 and phi : R+ -> R is sufficiently integrable. This paper investigates the fluctuations, as T -> infinity, of integral functionals of the form t -> integral(Tt)(0) P(X(s)) ds, in the case where P is any given polynomial function. It extends a study initiated in (Stoch. Dyn. 18 (2018) 1850028, 18), where only the quadratic case P(x) = x(2) and the convergence in the sense of finite-dimensional distributions were considered.