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Contents of PMS, Vol. 42, Fasc. 2,
pages 219 - 225
DOI: 10.37190/0208-4147.00071
Published online 20.9.2022
 

A remark on the exact laws of large numbers for ratios of independent random variables

P. Matuła

Let (Xn)n∈N and (Yn)n∈N be two sequences of i.i.d. random variables which are independent of each other and all have the distribution of a positive random variable ξ with density fξ. We study weighted strong laws of large numbers for the ratios of the form 1bn∑k=1nakXkYk in the cases when Eξ=∞ or limx→0+fξ(x)=0 or fξ is unbounded. This research complements some results known so far.

2010 AMS Mathematics Subject Classification: Primary 60F15; Secondary 60G50.

Keywords and phrases: almost sure convergence, law of large numbers, i.i.d. random variables.

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