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We prove the chain rule in the more general framework of the Wiener-Poissonspace, allowing us to obtain the so-called Nourdin-Peccati bound. From thisbound we obtain a second-order Poincare-type inequality that is useful in termsof computations. For completeness we survey these results on the Wiener space,the Poisson space, and the Wiener-Poisson space. We also give severalapplications to central limit theorems with relevant examples: linearfunctionals of Gaussian subordinated fields (where the subordinated field canbe processes like fractional Brownian motion or the solution of theOrnstein-Uhlenbeck SDE driven by fractional Brownian motion), Poissonfunctionals in the first Poisson chaos restricted to infinitely many \small"jumps (particularly fractional Levy processes) and the product of twoOrnstein-Uhlenbeck processes (one in the Wiener space and the other in thePoisson space). We also obtain bounds for their rate of convergence tonormality.

Normal Convergence Using Malliavin Calculus With Applications and Examples