On the second order Poincaré inequality and CLT on Wiener-Poisson space

Abstract

An upper bound for the Wasserstein distance is provided in the general framework of the Wiener-Poisson space. Is obtained from this bound a second order Poincaré-type inequality which is useful in terms of computations. For completeness sake, is made a survey of these results on the Wiener space, the Poisson space, and the Wiener-Poisson space, and showed several applications to central limit theorems with relevant examples: linear functionals of Gaussian subordinated field (where the subordinated field can be processes like fractional Brownian motion or the solution of the Ornstein-Uhlenbeck SDE driven by fractional Brownian motion), Poisson functionals in the first Poisson chaos restricted to \small" jumps (particularly fractional Lévy processes) and the product of two Ornstein-Uhlenbeck processes (one in the Wiener space and the other in the Poisson space). Also, are obtained bounds for their rate of convergence to normality.

References in corpus (2)

• Central limit theorems for sequences of multiple stochastic integrals
• On the orthogonal polynomials associated with a Lévy process

Cited by in corpus (2)

• Gamma limits and U-statistics on the Poisson space
• Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions