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...

A class of Volterra transforms, preserving the Wiener measure, with kernels of Goursat type is considered. Such kernels satisfy a self-reproduction property. We provide some results on the inverses of the associated Gramian matrices which lead to a new self-reproduction property. A connection to...