A note on the local time of fractional Brownian motion
The paper investigates the asymptotic behaviour of the local time at the origin of a \(q\)-dimensional fractional Brownian motion, when its index \(\gamma\) approaches the critical value \(1/q\). The main result of the article is a singular limit theorem proving that, under a suitable (temporally inhomogeneous) normalization, the considered local time of fractional Brownian motion converges in law to the inverse of an extremal process which appears in the extreme value theory.
scientific article; zbMATH DE number 1275654