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 as semimartingales in their own filtration. In particular we characterize those transformations which...

We show the existence, for any k E N, of processes which have the same k-marginals as Brownian motion, although they are not Brownian motions. For k = 4, this proves a conjecture of Stoyanov. The law P' of such a "weak Brownian motion of order k" can be constructed to be equivalent to Wiener...