Let ${\cal Q}$ be the set of equivalent martingale measures for a given process $S$, and let $X$ be a process which is a local supermartingale with respect to any measure in ${\cal Q}$. The optional decomposition theorem for $X$ states that there exists a predictable integrand $\varphi$ such...

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...