Convergence rate analysis in limit theorems for nonlinear functionals of the second Wiener chaos

Gi-Ren Liu

Stochastic Processes and their Applications, 2024, vol. 178, issue C

Abstract: This paper analyzes the distribution distance between random vectors from the analytic wavelet transform of squared envelopes of Gaussian processes and their large-scale limits. For Gaussian processes with a long-memory parameter below 1/2, the limit combines the second and fourth Wiener chaos. Using a non-Stein approach, we determine the convergence rate in the Kolmogorov metric. When the long-memory parameter exceeds 1/2, the limit is a chi-distributed random process, and the convergence rate in the Wasserstein metric is determined using multidimensional Stein’s method. Notable differences in convergence rate upper bounds are observed for long-memory parameters within (1/2,3/4) and (3/4,1).

Keywords: Analytic wavelet transform; Central limit theorems; Long-range dependence; Malliavin calculus; Multidimensional Stein’s method; Non-central limit theorems; Rate of convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104477

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