arXiv subjects

Qianqian Jiang

Publications and source records attributed to Qianqian Jiang.

6 recordsLinked to original sources

arXiv2026

Smoluchowski-Kramers approximation with Lévy noise in the Meyer--Zheng topology

We study the Smoluchowski-Kramers approximation for a stochastic wave equation with state-dependent damping on a bounded domain, driven by both a $Q$-Wiener process and a Lévy process with finite second moment. As $\varepsilon\to0$, we prove that $u^\varepsilon$ converges in distribution, in the Meyer-Zheng topology, to the unique weak solution of an overdamped stochastic parabolic equation. The proof relies on a nonlinear transformation associated with the damping coefficient, uniform energy estimates, and compactness arguments in the pseudo-path topology. We identify the limiting equation, which contains both the classical Gaussian noise-induced drift caused by state-dependent damping and an explicit jump correction generated by the Lévy noise. We show that the latter coincides exactly with the Marcus-to-Itô correction associated with the canonical jump flow induced by the nonlinear damping transformation.

math.PR↗

arXiv2026

Adaptive online kernel changepoint detection

We propose an adaptive online kernel-based changepoint detection method for streaming data that is capable of detecting a broad range of changes in the underlying data distribution. The method maintains a recursively-weighted reproducing kernel Hilbert space representation of observations and adaptively updates the forgetting factor through a gradient-based procedure driven by a maximum mean discrepancy-type statistic between the current observation and the weighted empirical distribution of the past. This self-tuning mechanism allows the detector to adapt its effective memory and responsiveness to changes in the underlying process. Simulation results demonstrate that the proposed method achieves strong detection performance across a wide range of distributional changes. Further, our proposed approach maintains constant computational and storage cost through recursive updates, and is very computationally efficient in comparison to competing methods. Experiments on both simulated data and benchmark real-world datasets show improved performance over several other leading kernel-based methods.

stat.ME↗

arXiv2025

On eigenvalues of a renormalized sample correlation matrix

This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under a unified framework where the dimension-to-sample size ratio $p/n\rightarrow c\in (0,\infty]$. Based on our CLT result, we propose an independence test statistic capable of operating effectively in both high and ultrahigh dimensional scenarios. Simulation experiments demonstrate the accuracy of theoretical results.

math.ST↗

arXiv2024

The Smoluchowski-Kramers approximation for a system with arbitrary friction depending on both state and distribution

A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the small mass limit. We obtain the limiting equation and, in particular, the addition drift terms that appear in the limiting equation are expressed in terms of the solutions to the Lyapunov matrix equation and Sylvester matrix equation. Furthermore, we provide the rate of convergence and extend the system to encompass more general interactions and noise.

math.PR↗

arXiv2024

On testing mean of high dimensional compositional data

We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test statistics which are suitable for detecting sparse signals. However, in this paper, we introduce a novel approach using sum-type test statistics which are capable of detecting weak but dense signals. By establishing the asymptotic independence between the max-type and sum-type test statistics, we further propose a combined max-sum type test to cover both cases. We derived the asymptotic null distributions and power functions for these test statistics. Simulation studies demonstrate the superiority of our max-sum type test statistics which exhibit robust performance regardless of data sparsity.

math.ST↗

arXiv2023

On eigenvalues of sample covariance matrices based on high dimensional compositional data

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under the high-dimensional regime where the data dimension increases to infinity proportionally with the sample size. The findings reveal that the limiting spectral distribution is the well-known Marchenko-Pastur law. The largest (or smallest non-zero) eigenvalue converges almost surely to the left (or right) endpoint of the limiting spectral distribution, respectively. Moreover, the linear spectral statistics demonstrate a Gaussian limit. Simulation experiments demonstrate the accuracy of theoretical results.

math.ST↗