Variance of partial sums of stationary sequences

• Autores: George Deligiannidis, Sergey Utev
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 5, 2013, págs. 3606-3616
• Idioma: inglés
• DOI: 10.1214/12-AOP772
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• Resumen

  • 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).