Construction of Brownian motion in the affine group

by Matyas Barczy (Debrecen) and Gyula Pap (Debrecen)

It is shown that a Gaussian Levy process (i.e., Levy process with vanishing Levy measure) in the affine group can be constructed by the help of one standard Wiener process, or two independent Wiener processes. The formula involves Ito integrals and reflects the group law. Moreover we will give a complete description of all possible supports for Gauss measures on the affine group.