We investigate various aspects of stochastic integration in finite von Neumann algebras. For integration with respect to a bounded
-martingale the idea of treating the integral as a bounded operator is developed. Several classes of integrable processes are defined, it turns out that some of them form a Banach or
*-algebra. We find representations of these algebras and establish relations between the von Neumann algebras generated by these representations. Finally, we characterize the range of the stochastic integration operator.
Barnett, C., Goldstein, S.
and Wilde, I. F.
, Quantum stopping times and Doob-Meyer decompositions,
J. Operator Theory35
Wilde I. F. , 'Quantum stopping times and Doob-Meyer decompositions' (1996) 35J. Operator Theory: 85-106.
Wilde I. F. Quantum stopping times and Doob-Meyer decompositionsJ. Operator Theory19963585106)| false