Work

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

Year: 2024

Type: article

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).

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2024.104477

Author: Gi-Ren Liu

Institutions: National Taiwan University, National Center for Theoretical Sciences, National Cheng Kung University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,420

Funders: National Science and Technology Council, National Center for Theoretical Sciences, National Science and Technology Council