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Aug 11, 2021 at 7:22 comment added Joe_Affine That makes sense, at first glance, the result looks very similar to Cramèr's Theorem in LD Theory...So I guess maybe it would appear embedded within that result's proof (I'll take a look); also thanks!
Aug 9, 2021 at 17:18 comment added Iosif Pinelis @Joe_Affine : Oops, I did miss the normalization. This is now fixed. I think this result is partly folklore, which can be found in books on large deviations, except that they seem to be usually focused on asymptotics, rather than inequalities. Here the main difficulty was converting the two rates $I_\pm$ into one rate $I$.
Aug 9, 2021 at 17:12 history edited Iosif Pinelis CC BY-SA 4.0
added 9 characters in body
Aug 9, 2021 at 16:40 vote accept Joe_Affine
Aug 9, 2021 at 16:36 history answered Iosif Pinelis CC BY-SA 4.0