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The aim of this work is to provide a simpler proof of the Boue- Dupuis variational representation for positive functionals of a Brownian mo- tion. Earlier proofs have relied on results concerning measurable selections whereas our approach uses functional stochastic differential equations. An application of this variational formula to a Wentzell-Freidlin type large devi- ations result in the context of non-Newtonian fluid flow is briefly discussed.

A representation for positive functionals of a Brownian motion and an application