In this paper we give some characterizations of BMOA functions in terms of Kahler diffusions and Carleson measures on the unit ball in C n n1 (see Theorem 1). This result implies Carleson measure characterizations of BMOA obtained recently by Choa and Choe [2] and Stanton [19]. Furthermore, as a corollary we prove that the spaces BMOA and BMO are isomorphic to closed complemented subspaces of a space of BMO martingales. From this it follows a non-isotropic version of Garnett-Jones theorem.