Strong Laws and Summability for Sequences of $\phi$-Mixing Random Variables in Banach Spaces

Abstract

In this note the almost sure convergence of stationary, $\varphi$-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.