Electronic Communications in Probability

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

Rädiger Kiesel

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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.

Article information

Electron. Commun. Probab., Volume 2 (1997), paper no. 3, 27-41.

Accepted: 14 May 1997
First available in Project Euclid: 26 January 2016

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Zentralblatt MATH identifier

Primary: 60F15: Strong theorems
Secondary: 40G05: Cesàro, Euler, Nörlund and Hausdorff methods 40G10: Abel, Borel and power series methods

Strong Laws $varphi$-mixing Summability

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Kiesel, Rädiger. Strong Laws and Summability for Sequences of $\phi$-Mixing Random Variables in Banach Spaces. Electron. Commun. Probab. 2 (1997), paper no. 3, 27--41. doi:10.1214/ECP.v2-982. https://projecteuclid.org/euclid.ecp/1453832498

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