A note on the local time of fractional Brownian motion (Q1283446)

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.