ON THE LOCAL AND ASYMPTOTIC-BEHAVIOR OF BROWNIAN-MOTION ON SIMPLY CONNECTED NILPOTENT LIE-GROUPS

The aim of this paper is to study the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups. We carry ov er a qualitative version of the Erdos-Renyi law of large numbers for B rownian motion to simply connected step 2-nilpotent Lie groups. The me thod 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-Freidli n theory as in Baldi.((1, 2))