Precise asymptotics in the law of logarithm under dependence assumptions

In a recent paper by Spătaru [Precise asymptotics for a series of T.L. Lai, Proc. Amer. Math. Soc. 132 (11) (2004) 3387–3395] a precise asymptotics in the law of the logarithm for sequence of i.i.d. random variables has been established. In this paper we show that there is an analogous result for strictly stationary φ-mixing sequence. To prove this result, we have to use a different method. One of our main tools is the Gaussian approximation technique.