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Let $X_1, X_2, ...$ be a sequence of i.i.d. random variables such that $\mathbb{E}|X_1|^r < \infty$ for some $r > 1$. If b_n is a sequence such that $b_n \to \infty$ as $n \to \infty$ then $\mathbb{E} [|X_1|^r . I_{|X_n| > b_n}] \to 0$ as $n \to \infty$. Does there exist any result which gives the asymptotics for $\mathbb{E} [|X_1|^r . I_{|X_n| > b_n}]$, that is, what is the speed of convergence of $\mathbb{E} [|X_1|^r . I_{|X_n| > b_n}]$?

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    Hi, your notation was quite ambiguous. I have tried to put the text into LaTeX for you but if anything look wrong just shout and I'll edit it again (or you could take the opportunity to learn some LaTeX yourself :) )2012-11-23
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    The LaTeX text is fine! Maybe the symbol "{" and "}" is missing in the set of the indicator function. Some hint for this? Jimmy2012-11-24
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    If you go to edit the post you should just put \{ and \} around the set. The backslash tells the Latex interpreter to treat the brace as a brace and not as a special character.2012-11-25

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