Innovations informational equivalence for a class of observations with independent non-Gaussian noise

The problem of innovations informational equivalence for observations with non-Gaussian additive noise is addressed. It is assumed that the additive noise is a non-Gaussian continuous martingale with an almost surely absolutely continuous quadratic covariation process. Under the assumptions of stochastic independence between the signal and the noise and of square integrability conditions on them, it is shown that the non-Gaussian innovations process, i.e., a non-Gaussian martingale adapted to the observation, is informationally equivalent to the observation