Timeline for Large deviations estimate for arbitrary continuous function

Current License: CC BY-SA 4.0

15 events

when toggle format	what		by	license	comment
Jun 6, 2020 at 1:36	history	edited	leo monsaingeon	CC BY-SA 4.0	minor mathjaxing for readability
Jun 5, 2020 at 16:57	comment	added	ABIM		Yes I'm noting this now... and I think this also has the property that $X_t^{x,\epsilon}$ can be close to any other function with positive probability, which is nice.
Jun 5, 2020 at 16:55	comment	added	Iosif Pinelis		What about letting $X_t^{x,\epsilon}:=f(x)$ for all $t,x$ (with $\mu=0$), and then modifying $X$ by choosing $\Sigma>0$ to be arbitrarily small?
Jun 5, 2020 at 16:11	comment	added	ABIM		True, I have fixed this. Thank you Pierre.
Jun 5, 2020 at 16:10	history	edited	ABIM	CC BY-SA 4.0	added 5 characters in body
Jun 5, 2020 at 16:09	comment	added	Pierre PC		If the initial condition is $x$, and $f(x)\neq x$, then $X^{x,\epsilon}$ cannot be close to $f(x)$ for $t$ small.
Jun 5, 2020 at 16:07	comment	added	ABIM		The supremum should be over both t and x.
Jun 5, 2020 at 16:06	history	edited	ABIM	CC BY-SA 4.0	added 21 characters in body
Jun 5, 2020 at 16:04	history	edited	YCor	CC BY-SA 4.0	removed capitals from title
Jun 5, 2020 at 16:04	history	undeleted	user142150
Jun 5, 2020 at 16:04	history	deleted	user142150		via Vote
Jun 5, 2020 at 15:58	comment	added	Iosif Pinelis		You have $x$ under the probability sign. What is the quantifier on $x$ there?
Jun 5, 2020 at 15:56	comment	added	Pierre PC		What is your initial condition for $X^{x,\epsilon}$? Is it $x$? Then $f$ must go from $\mathbb R^n$ to itself, right?
Jun 5, 2020 at 15:47	comment	added	ABIM		I think Freidlin-Wentzell theory can be used but I'm not sure it will give you a positive probability...
Jun 5, 2020 at 15:45	history	asked	ABIM	CC BY-SA 4.0