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Aug 1, 2011 at 17:23 comment added Yaakov Baruch I agree with the vote to close, but I would like to first select Leonid Petrov's answer if he posted it as such.
Aug 1, 2011 at 15:10 history edited Michael Hardy CC BY-SA 3.0
two more small notation edits
Jul 31, 2011 at 11:37 comment added Yaakov Baruch @Leonid: I think your comment is the answer to the question (or at least the INTENDED question).
Jul 31, 2011 at 11:23 history edited Yaakov Baruch CC BY-SA 3.0
added 4 characters in body
Jul 31, 2011 at 11:23 comment added Yaakov Baruch Gerry Myerson: yes, I edited accordingly. @Ricky Demer: I replaced "hit" with "crossed" - I hope that clarifies that I'm not looking for equality of two functions, but for $f$'s such that $\limsup |S_n|/f(n) \ge 1$ with probability 1
Jul 31, 2011 at 11:09 history edited Yaakov Baruch CC BY-SA 3.0
added 9 characters in body
Jul 31, 2011 at 9:21 comment added Gerry Myerson Does it makes sense for a limit on $n$ to be a function of $n$? Perhaps you mean the expected value is asymptotic to that function of $n$?
Jul 31, 2011 at 9:18 comment added user5810 How is $f(x) = \sqrt{x}$ clearly if $F\hspace{.03 in}$? Among other things, $f$ can only be hit by $|S_n|$ at perfect squares.
Jul 31, 2011 at 8:36 comment added Leonid Petrov Have you heard about the Law of iterated logarithm? en.wikipedia.org/wiki/Law_of_the_iterated_logarithm I think that this may help you.
Jul 31, 2011 at 8:28 history edited Yaakov Baruch CC BY-SA 3.0
edited title
Jul 31, 2011 at 8:17 history asked Yaakov Baruch CC BY-SA 3.0