Quantum stochastic integrals under standing hypotheses (Q1091675)

We study the meaning of stochastic integrals when the integrator is a quantum stochastic process which is not quite a martingale, in that it obeys estimates of the type advocated by \textit{E. J. McShane} [Stochastic calculus and stochastic models. (1974; Zbl 0292.60090)] in the classical case. We define the integral and solve stochastic differential equations when the von Neumann algebra is finite and when it has a cyclic and separating state or weight. When conditional expectations exist, a quantum martingale continuity theorem is proved.