Gi-Ren Liu

activity

20102025

most citedPhase Retrieval with One or Two Diffraction Patterns by Alternating Projection with Null Initialization

12 citations · 16 across the 12 of their papers we have counts for

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5 papers · 1 filter

math.PR2023

Gaussian Approximation for the Moving Averaged Modulus Wavelet Transform and its Variants

Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu

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 wo…

math.PR2021

When Scattering Transform Meets Non-Gaussian Random Processes, a Double Scaling Limit Result

Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu

We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simulta…

math.PR2021

Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes

Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu

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…

math.PR2014

Multi-scaling Limits for Relativistic Diffusion Equations with Random Initial Data

Gi-Ren Liu, Narn-Rueih Shieh

Let $u (t, x), t > 0, x \in R^{n},$ be the spatial-temporal random field arising from the solution of a relativistic diffusion equation with the spatial-fra…

math.PR2010

Homogenization of Fractional Kinetic Systems with Random Initial Data

Gi-Ren Liu, Narn-Rueih Shieh

Let $w (t, x) := (u, v) (t, x), t > 0, x \in R^{n},$ be the $R^{2}$ -valued spatial-temporal random field $w = (u, v)$ arising from a certain two-equation system…