Resumen de Variance of partial sums of stationary sequences

George Deligiannidis, Sergey Utev

• Let X1,X2,… be a centred sequence of weakly stationary random variables with spectral measure F and partial sums Sn=X1+⋯+Xn. We show that var(Sn) is regularly varying of index γ at infinity, if and only if G(x):=∫x−xF(dx) is regularly varying of index 2−γ at the origin (0<γ<2).