Brownian representations of cylindrical continuous local martingales

Abstract

In this paper, we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular, we consider the class of cylindrical martingales with closed operator-generated covariations. We also prove that for every cylindrical continuous local martingale [Formula: see text] there exists a time change [Formula: see text] such that [Formula: see text] is Brownian representable.