Let I be a countable index set, and let P be a probability measure on C[0, 1]I such that the coordinate process satisfies an infinite-dimensional stochastic differential equation dX = dW+b(X,t)dt. In contrast to the finite-dimensional case, the time reversed process cannot always be described by...

We study the long run behaviour of interactive Markov chains on infinite product spaces. In view of microstructure models of financial markets, the interaction has both a local and a global component. The convergence of such Markov chains is analyzed on the microscopic level and on the...

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...