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What, if anything, do we know about the rate of convergence of of the mean of identically distributed, independent or stationary random variables drawn from a distribution with a finite mean and infinite or nonexistent variance?

I have asked a separate question about the conditions under which the mean of such variables do converge. In answering this question, you may assume that such conditions, whatever they are, hold.

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  • $\begingroup$ Can you please link to your other question. $\endgroup$ – Ben Apr 17 '18 at 2:32
  • $\begingroup$ I can't help much but there's probably some version of a WLLN that doesn't require finite variance. So, if you can find that WLLN, the proof of it will probably answer your question. I don't know or I would give you a name but there are so many that I bet one of them relaxes the finite variance assumption. $\endgroup$ – mlofton Jan 13 at 4:50

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