%0 Journal Article %T Symmetry and Time Changed Brownian Motions %A Jos¨¦ Fajardo %A Ernesto Mordecki %J Mathematics %D 2008 %I arXiv %X In this paper we examine which Brownian Subordination with drift exhibits the symmetry property introduced by Fajardo and Mordecki (2006). We obtain that when the subordination results in a L\'evy process, a necessary and sufficient condition for the symmetry to hold is that drift must be equal to -1/2. %U http://arxiv.org/abs/0810.4271v1