Abstract
The aim of this paper is to study the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups. We carry over a qualitative version of the Erdos-Renyi law of large numbers for Brownian motion to simply connected step 2-nilpotent Lie groups. The method applied gives rise to a proof for qualitative results concerning the modulus of continuity of Brownian motion on simply connected step 3-resp. step 2-nilpotent Lie groups without using the Ventsel-Freidlin theory as in Baldi.
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