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.
[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.
A positive-valued, unbounded probability distribution
may be called subexponential if its tails are heavy enough so that[2]: Definition 1.1 See Heavy-tailed distribution § Subexponential distributions.
Contrariwise, a random variable may also be called subexponential if its tails are sufficiently light to fall off at an exponential or faster rate.