Resumen de Recurrence rates and hitting-time distributions for random walks on the line

Françoise Pène, Benoît Saussol, Roland Zweimüller

• We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as ε→0, of the return time to (−ε,ε). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x−ε,x+ε) with arbitrary x∈R.