2011/04/11 by Juan Víquez, Víquez, Juan
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #advanced mathematical theories #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1104.1837
openalex publication_date 2011/04/11 · arxiv created 2012/04/26 · arxiv updated 2012/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.