> specific problem classes (those with α ≤ 1),
For the layman, what does α mean here?
I'm sure this is a reference to alpha stable distributions: https://en.m.wikipedia.org/wiki/Stable_distribution
Most of these don't have finite moments and are hard to do inference on with standard statistical tools. Nassim Taleb's work (Black Swan, etc.) is around these distributions.
But I think the argument of OP in this section doesn't hold.
I'm sure this is a reference to alpha stable distributions: https://en.m.wikipedia.org/wiki/Stable_distribution
Most of these don't have finite moments and are hard to do inference on with standard statistical tools. Nassim Taleb's work (Black Swan, etc.) is around these distributions.
But I think the argument of OP in this section doesn't hold.