Timeline for Maximal inequality for the average of i.i.d. random variables

Current License: CC BY-SA 4.0

14 events

when toggle format	what		by	license	comment
Nov 15, 2018 at 1:40	vote	accept	Xiao
Nov 14, 2018 at 20:02	answer	added	fedja		timeline score: 7
Nov 14, 2018 at 1:16	comment	added	fedja		@MattF. The Gaussian case is not too difficult (if one doesn't care about the best $\alpha$). The general case can, probably, be obtained by the CLT approximation, but the resulting argument looks too ugly to post ;-(
Nov 13, 2018 at 22:44	history	edited	Xiao	CC BY-SA 4.0	added 14 characters in body
Nov 13, 2018 at 19:58	comment	added	fedja		Something more should be assumed in general (because if all $Z_j=0$ with probability $1$, then you are out of luck). On the other hand, if you have bounded density and quickly decaying tails (as it seems to be the case), it becomes an interesting question.
Nov 13, 2018 at 18:56	comment	added	user44143		If Z is normal, the left hand side could be called “the price of a binary option with a discrete Asian barrier on a Brownian-motion asset”. Unfortunately the papers on “discrete Asian barrier options” don’t seem to address this case.
Nov 13, 2018 at 18:42	history	edited	Xiao	CC BY-SA 4.0	added 9 characters in body
Nov 13, 2018 at 18:18	history	edited	Xiao	CC BY-SA 4.0	added 2 characters in body
Nov 13, 2018 at 17:01	history	edited	Xiao	CC BY-SA 4.0	deleted 40 characters in body; edited title
Nov 13, 2018 at 6:43	history	edited	Xiao	CC BY-SA 4.0	added 32 characters in body
Nov 13, 2018 at 2:44	history	edited	Xiao	CC BY-SA 4.0	added 24 characters in body
Nov 13, 2018 at 2:33	history	edited	Xiao	CC BY-SA 4.0	added 692 characters in body
Nov 13, 2018 at 2:01	history	edited	Xiao	CC BY-SA 4.0	deleted 121 characters in body
Nov 12, 2018 at 22:22	history	asked	Xiao	CC BY-SA 4.0