It seems that the proof I am reading of the Martingale Representation Theorem,
"A square integrable RCLL martingale which is adapted to the augmented filtration of a Brownian Motion must be an Ito Integral wrt BM."
does not use any properties of Brownian Motion besides that the augmented filtration satisfies the usual conditions.
So for example, it should be true that the martingale representation theorem holds if $W$ is replaced by any strong markov process martingale.
Does anyone know of a result like this or do you know if some special property of Brownian motion is necessary for this result?