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Based on the Stein method and a general integration by parts framework we derive various bounds on the distance between probability measures. We show that this framework can be implemented on the Poisson space by covariance identities obtained from the Clark-Ocone representation formula and derivation operators. Our approach avoids the use of the inverse of the Ornstein Uhlenbeck operator as in the existing literature, and also applies to the Wiener space.

Probability approximation by Clark-Ocone covariance representation