Proceedings of the Royal Society of Edinburgh, section A (Mathematics), volume 120 (1992), pages 267-282.

We give an expression for the *n*-th moment of certain Itô integrals. The
integrands considered are nonanticipating functionals of the form
*s*
®
**a**(*s*, *X*_{s})
where **a** is a measurable time-dependent vector field in space satisfying mild
regularity conditions, and *X*_{s} is standard translated Brownian motion.
The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger
semigroups.

We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

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