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

Minor revision

References in corpus (2)

• Stochastic integration in UMD Banach spaces
• Cylindrical continuous martingales and stochastic integration in infinite dimensions