Stochastic integrals in an arbitrary probability gauge space

Abstract

In § 7 of [1] we described how a stochastic integral of non-commuting process cesan be constructed. This was achieved via a Doob-Meyer decomposition for the square of a self-adjoint L2-martingale. We introduced a ‘condition D'’ derived from the lsquo;class D’ of stochastic process theory, and showed that if the square of a self-adjoint L2-martingale satisfies this condition then it has a decomposition of the Doob-Meyer type. The purpose of this paper is to extend the results of § 7 of [1] and to introduce another construction of the stochastic integral that does not employ condition D.