A growth rate is said to be infra-exponential or subexponential if it is dominated by all exponential growth rates, however great the doubling time. A continuous function with infra-exponential growth rate will have a Fourier transform that is a Fourier hyperfunction.[1]
Examples of subexponential growth rates arise in the analysis of algorithms, where they give rise to sub-exponential time complexity, and in the growth rate of groups, where a subexponential growth rate implies that a group is amenable.
\calD
\limx\to+infty
{\BbbP | |
(X |
1+X2>x)}{{\BbbP}(X>x)}=2, X1,X2,X\sim{\calD}, X1,X2\hbox{independent.}