Quantum stochastic integrals under standing hypotheses

C. Barnett, R. F. Streater and I. F. Wilde, J. of Mathematical Anal. and Applications, 127, 181-192, 1987.

ABSTRACT

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 McShane 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.

REMARKS

This is a generalisation of quantum stochastic integrals using martingales; it was introduced because in physics the noise is usually coloured, as in my earlier paper.