arXiv subjects

Dongzhou Huang

Publications and source records attributed to Dongzhou Huang.

8 recordsLinked to original sources

arXiv2026

Queueing models with random resetting

We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models under the first-come first-served (FCFS) discipline. The Markovian models include M/M/$r$ and M/M/1+M queues with random resetting, in which a continuous-time Markov chain is formulated, with transitions including a resetting to state zero in addition to arrivals and services. We explicitly characterize the stationary distributions of the queueing processes in these models by using parting balance equations. We derive expressions for standard performance measures such as the delay probability, expected queue length and waiting time, as well as probability of a customer completing service before resetting in the M/M/$r$ model, and probability of abandonment before service or resetting in the M/M/1+M model. The non--Markovian models include GI/GI/1, GI/GI/$r$ and GI/GI/$\infty$ queues with random resetting to state zero at arrival times. For GI/GI/1 and GI/GI/$r$ queues under the FCFS discipline, we introduce modified Lindley and Kiefer--Wolfowitz recursions, respectively. Using an operator representation for these recursions, we characterize the stationary distributions via convergent series, as solutions to the modified Wiener--Hopf equations. For GI/GI/$\infty$ queues with resettings, we utilize a version of the Kiefer--Wolfowitz recursion, and also characterize the corresponding stationary distribution.

math.PR↗

arXiv2026

Wasserstein convergence rates for empirical measures of point processes

In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures and, based on this metric, define a Wasserstein distance between point processes. We then employ it to study the convergence rate of the empirical measures of point processes, which serves as a natural tool for identifying the distribution of the underlying point process. Furthermore, we derive concentration results. These theoretical results provide constructive tools for hypothesis testing and statistical inference for point processes. The applicability of our results is demonstrated through several practical examples.

math.ST↗

arXiv2025

Variational Estimators for Node Popularity Models

Node popularity is recognized as a key factor in modeling real-world networks, capturing heterogeneity in connectivity across communities. This concept is equally important in bipartite networks, where nodes in different partitions may exhibit varying popularity patterns, motivating models such as the Two-Way Node Popularity Model (TNPM). Existing methods, such as the Two-Stage Divided Cosine (TSDC) algorithm, provide a scalable estimation approach but may have limitations in terms of accuracy or applicability across different types of networks. In this paper, we develop a computationally efficient and theoretically justified variational expectation-maximization (VEM) framework for the TNPM. We establish label consistency for the estimated community assignments produced by the proposed variational estimator in bipartite networks. Through extensive simulation studies, we show that our method achieves superior estimation accuracy across a range of bipartite as well as undirected networks compared to existing algorithms. Finally, we evaluate our method on real-world bipartite and undirected networks, further demonstrating its practical effectiveness and robustness.

stat.ML↗

arXiv2025

Exact and asymptotic distribution theory for the empirical correlation of two AR(1) processes with Gaussian increments

This paper begins with a study of the exact distribution of the empirical correlation of two independent AR(1) processes with Gaussian increments. We proceed to develop rates of convergence for the distribution of the scaled empirical correlation to the standard Gaussian distribution in both Wasserstein distance and Kolmogorov distance. Given $n$ data points, we prove the convergence rate in Wasserstein distance is $n^{-1/2}$ and the convergence rate in Kolmogorov distance is $n^{-1/2} \sqrt{\ln n}$. We conclude by extending these results to two AR(1) processes with correlated Gaussian increments.

math.ST↗

arXiv2023

The existence of the least favorable noise

Suppose that a random variable $X$ of interest is observed. This paper concerns "the least favorable noise" $\hat{Y}_ε$, which maximizes the prediction error $E [X - E[X|X+Y]]^2 $ (or minimizes the variance of $E[X| X+Y]$) in the class of $Y$ with $Y$ independent of $X$ and $\mathrm{var} Y \leq ε^2$. This problem was first studied by Ernst, Kagan, and Rogers ([3]). In the present manuscript, we show that the least favorable noise $\hat{Y}_ε$ must exist and that its variance must be $ε^2$. The proof of existence relies on a convergence result we develop for variances of conditional expectations. Further, we show that the function $\inf_{\mathrm{var} Y \leq ε^2} \, \mathrm{var} \, E[X|X+Y]$ is both strictly decreasing and right continuous in $ε$.

math.ST↗

arXiv2021

Yule's "nonsense correlation" for Gaussian random walks

The purpose of this paper is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks as well as implicit formulas for higher moments. The proofs are based on a symbolically tractable integro-differential representation formula for the moments of any order in a class of empirical correlations, first established by Ernst et al. (2019) and investigated previously in Ernst et al. (2017). We also provide rates of convergence of the empirical correlation of two independent Gaussian random walks to the empirical correlation of two independent Wiener processes, by exploiting the explicit nature of the computations used for the moments. At the level of distributions, in Wasserstein distance, the convergence rate is the inverse $n^{-1}$ of the number of data points $n$. This holds because we represent and couple the discrete and continuous correlations on a common probability space, where we establish convergence in $L^1$ at the rate $n^{-1}$.

math.PR↗

arXiv2021

Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant

We consider an obliquely reflected Brownian motion $Z$ with positive drift in a quadrant stopped at time $T$, where $T:=\inf \{ t>0 : Z(t)=(0,0) \}$ is the first hitting time of the origin. Such a process can be defined even in the non-standard case where the reflection matrix is not completely-$\mathcal{S}$. We show that in this case the process has two possible behaviors: either it tends to infinity or it hits the corner (origin) in a finite time. Given an arbitrary starting point $(u,v)$ in the quadrant, we consider the escape (resp. absorption) probabilities $\mathbb{P}_{(u,v)}[T=\infty]$ (resp. $\mathbb{P}_{(u,v)}[T<\infty]$). We establish the partial differential equations and the oblique Neumann boundary conditions which characterize the escape probability and provide a functional equation satisfied by the Laplace transform of the escape probability. We then give asymptotics for the absorption probability in the simpler case where the starting point in the quadrant is $(u,0)$. We exhibit a remarkable geometric condition on the parameters which characterizes the case where the absorption probability has a product form and is exponential. We call this new criterion the dual skew symmetry condition due to its natural connection with the skew symmetry condition for the stationary distribution. We then obtain an explicit integral expression for the Laplace transform of the escape probability. We conclude by presenting exact asymptotics for the escape probability at the origin.

math.PR↗

arXiv2020

The rencontre problem

Let $\left\{X^{1}_k\right\}_{k=1}^{\infty}, \left\{X^{2}_k\right\}_{k=1}^{\infty}, \cdots, \left\{X^{d}_k\right\}_{k=1}^{\infty}$ be $d$ independent sequences of Bernoulli random variables with success-parameters $p_1, p_2, \cdots, p_d$ respectively, where $d \geq 2$ is a positive integer, and $ 0<p_j<1$ for all $j=1,2,\cdots,d.$ Let \begin{equation*} S^{j}(n) = \sum_{i=1}^{n} X^{j}_{i} = X^{j}_{1} + X^{j}_{2} + \cdots + X^{j}_{n}, \quad n =1,2 , \cdots. \end{equation*} We declare a "rencontre" at time $n$, or, equivalently, say that $n$ is a "rencontre-time," if \begin{equation*} S^{1}(n) = S^{2}(n) = \cdots = S^{d}(n). \end{equation*} We motivate and study the distribution of the first (provided it is finite) rencontre time.

math.PR↗