Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Eden, Richard¹  Viquez, Juan¹ 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

关键词: Malliavin calculus;    Stein's method;    Pearson distribution;    Convergence in distribution;   

DOI  :  10.1016/j.spa.2014.09.001

来源: Elsevier

【 摘 要 】

Given a reference random variable, we study the solution of its Stein equation and obtain universal bounds on its first and second derivatives. We then extend the analysis of Nourdin and Peccati by bounding the Fortet-Mourier and Wasserstein distances from more general random variables such as members of the Exponential and Pearson families. Using these results, we obtain non-central limit theorems, generalizing the ideas applied to their analysis of convergence to Normal random variables. We do these in both Wiener space and the more general Wiener Poisson space. In the former space, we study conditions for convergence under several particular cases and characterize when two random variables have the same distribution. In the latter space we give sufficient conditions for a sequence of multiple (Wiener Poisson) integrals to converge to a Normal random variable. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free