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

Rädiger Kiesel (University of London)

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.

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Pages: 27-41

Publication Date: May 14, 1997

DOI: 10.1214/ECP.v2-982

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