# Limit laws for maximal standardized increment of a random walk

vendredi 14 juin 2013, 13h30 - 14h15

We investigate the limit laws for the maximal standardized increment of a random walk. We assume that the jumps are formed by i.i.d. random variables, the distribution of which has finite Laplace transform.The case that the jumps are Gaussian has been addressed by Siegmund and Venkatraman (1995). For general distributions, our results reveal a more subtle picture: the limit law being always Gumbel, the normalization sequence depends on the distribution through their Laplace transform. In particular, we distinguish 4 different cases.

If time permits, we talk about some work in progress on similar problems with i.i.d. heavy-tailed random variables.

Joint work with Zakhar Kabluchko (Ulm University)