On weak invariance principles for sums of dependent random functionals

Given a sequence of random functionals {Xk(u)}k∈Z∈L2[0,1], the normalized partial sum-process Sn(t,u)=n−1/2(X1(u)+⋯+X⌊nt⌋(u)), t,u∈[0,1] is considered. Given two moments and a fairly general dependence structure, a weak invariance principle is established, extending a recent result of Berkes et al. (2013).