Maller, R. A. - In: Stochastic Processes and their Applications 10 (1980) 1, pp. 65-73
We show that if Xi is a stationary sequence for which Sn/Bn converges to a finite non zero random variable of constant sign, where Sn=X1+X2+...+Xn and Bn is a sequence of constants, then Bn is regularly varying with index 1. If in addition [Sigma]P(X1Bn is finite, then EX1 is finite, and if in...