Limit theorems for mixing sequences without rate assumptions

Abstract

We extend Lévy’s classical criterion for a sequence of independent identically distributed random variables to belong to the domain of partial attraction of a nondegenerate Gaussian law to stationary $\phi$-mixing sequences. We also extend some results of Kesten and of Kuelbs and Zinn on the LIL behavior of independent identically distributed random variables to stationary $\phi$-mixing sequences. No assumptions on the rate of decay for the mixing coefficient are made.