Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading

Motivated by the Kyle–Back model of “insider trading”, we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition, i.e., their Doob–Meyer decomposition as semimartingales in their own filtration. In particular we characterize those transformations which generate again a Brownian motion.