Published December 1988
| public
Journal Article
Laws of large numbers for dependent non-identically distributed random variables
- Creators
- Andrews, Donald W. K.
Abstract
This paper provides L^1 and weak laws of large numbers for uniformly integrable L^1-mixingales. The L^1-mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, φ(.), ρ(.), and α(.) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L^1-near epoch dependent, and mixingale sequences and triangular arrays. The random variables need not possess more than one finite moment and the L^1-mixingale numbers need not decay to zero at any particular rate. The proof of the results is remarkably simple and completely self-contained.
Additional Information
© 1988 Cambridge University Press. I would like to thank the referees, Hal White, and In Choi for helpful comments, the California Institute of Technology for their hospitality while this research was undertaken, and the Alfred P. Sloan Foundation and the National Science Foundation for their financial support through a Research Fellowship and Grant SES-8618617, respectively. Formerly SSWP 645.Additional details
- Eprint ID
- 83122
- Resolver ID
- CaltechAUTHORS:20171109-164301183
- SES-8618617
- NSF
- Alfred P. Sloan Foundation
- Created
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2017-11-16Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field