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

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  • Liu, Gi-Ren

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).

Suggested Citation

  • Liu, Gi-Ren, 2024. "Convergence rate analysis in limit theorems for nonlinear functionals of the second Wiener chaos," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001832
    DOI: 10.1016/j.spa.2024.104477
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