Electronic Communications in Probability

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

Rädiger Kiesel

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1453832498

Digital Object Identifier
doi:10.1214/ECP.v2-982

Mathematical Reviews number (MathSciNet)
MR1448323

Zentralblatt MATH identifier
0890.60026

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

Keywords
Strong Laws $varphi$-mixing Summability

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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