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

GR Liu - Stochastic Processes and their Applications, 2024 - Elsevier
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 …

Asymptotic analysis of higher-order scattering transform of Gaussian processes

GR Liu, YC Sheu, HT Wu - Electronic Journal of Probability, 2022 - projecteuclid.org
We analyze the scattering transform with the quadratic nonlinearity (STQN) of Gaussian
processes without depth limitation. STQN is a nonlinear transform that involves a sequential …

Central and noncentral limit theorems arising from the scattering transform and its neural activation generalization

GR Liu, YC Sheu, HT Wu - SIAM Journal on Mathematical Analysis, 2023 - SIAM
Motivated by the analysis of complicated time series, we examine a generalization of the
scattering transform that includes broad neural activation functions. This generalization is …

Gaussian approximation for the moving averaged modulus wavelet transform and its variants

GR Liu, YC Sheu, HT Wu - Applied and Computational Harmonic Analysis, 2025 - Elsevier
The moving average of the complex modulus of the analytic wavelet transform provides a
robust time-scale representation for signals to small time shifts and deformation. In this work …