Strong laws for associated random variables |
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Authors: | Tonguç Çağın |
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Affiliation: | Department of Mathematics, CMUC, University of Coimbra, Coimbra, Portugal |
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Abstract: | We study the almost sure convergence and rates of weighted sums of associated random variables under the classical assumption of existence of Laplace transforms. This assumption implies the existence of every moment, so we address the same problem assuming a suitable decrease rate on tail joint probabilities which only implies the existence of finitely many moments, proving the analogous characterizations of convergence and rates. Still relaxing further the assumptions on moment existence, we also prove a Marcinkiewicz–Zygmund for associated variables without means, complementing existing results for this dependence structure. |
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Keywords: | Almost sure convergence association convergence rates exponential inequalities Marcinkiewicz–Zygmund law |
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