  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 $M$ there exists a time change
$\tau$ such that $M\circ \tau$ is Brownian representable.

Probability;Functional Analysis