A law of the iterated logarithm for geometrically weighted martingale difference sequences (Q1322913)

Let \(Y_ n\), \(n\geq 1\), be a stationary and ergodic martingale difference sequence with \(E(Y^ 2_ 0)=1\), and for \(\beta<1\) set \(\xi(\beta)= \sum_{n=0}^ \infty \beta^ n Y_ n\). It is shown that the random variables \(\xi(\beta)\), when suitably normalized, obey a law of the iterated logarithm and a central limit theorem as \(\beta \nearrow 1\).