In this paper we get some results about the asymptotic behaviour of the sequence
Πn = 1 + X1 + X1X2 + X1X2X3 + ...
where {Xn}n=1 ∞ are i.i.d. random variables. Strong limit laws, Central limit theorem and Iterated Logarithm law are obtained, after an analysis of the convergence of Πn. Rates of convergence are also given.
@article{urn:eudml:doc:40425, title = {Sumas de productos de variables aleatorias independientes igualmente distribuidas (V.A.I.I.D.).}, journal = {Trabajos de Estad\'\i stica}, volume = {1}, year = {1986}, pages = {140-150}, zbl = {0658.60056}, language = {es}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40425} }
Vélez, Ricardo; Hernández, Víctor. Sumas de productos de variables aleatorias independientes igualmente distribuidas (V.A.I.I.D.).. Trabajos de Estadística, Tome 1 (1986) pp. 140-150. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40425/