On Weak Invariance Principles for Partial Sums

Given a sequence of random functionals {Xk(u)}k∈Z, u∈Id, d≥1, the normalized partial sums Sˇnt(u)=n−1/2(X1(u)+⋯+X⌊nt⌋(u)), t∈[0,1] and its polygonal version Snt(u) are considered under a weak dependence assumption and p>2 moments. Weak invariance principles in the space of continuous functions and càdlàg functions are established. A particular emphasis is put on the process Sˇnt(θ^), where θ^→Pθ, and weaker moment conditions (p=2 if d=1) are assumed