A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals
Let \(X_ 1,X_ 2,..\). be i.i.d. and positive random variables and put \[ N(t)=\max \{k: X_ 1+...+X_ k\leq t\}. \] If the tails of \(X_ i\) are regularly varying with index -1 then it is known that N(t), suitably normalized, tends in distribution to a stable law of order 1 as \(t\to \infty\). The authors give an alternative expression for the normalizing functions and discuss related conjugation concepts.
scientific article; zbMATH DE number 4028570