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- W2042803991 abstract "We use our maximum inequality for $p$-th order random variables ($p>1$) to prove a strong law of large numbers (SLLN) for sequences of $p$-th order random variables. In particular, in the case $p=2$ our result shows that $sum f(k)/k < infty$ is a sufficient condition for SLLN for $f$-quasi-stationary sequences. It was known that the above condition, under the additional assumption of monotonicity of $f$, implies SLLN (Erdos (1949), Gal and Koksma (1950), Gaposhkin (1977), Moricz (1977)). Besides getting rid of the monotonicity condition, the inequality enables us to extend thegeneral result to $p$-th order random variables, as well as to the case of Banach-space-valued random variables." @default.
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- W2042803991 date "2005-01-01" @default.
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- W2042803991 title "Strong Law of Large Numbers Under a General Moment Condition" @default.
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- W2042803991 doi "https://doi.org/10.1214/ecp.v10-1156" @default.
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