arXiv subjects

Nhu Nguyen

Publications and source records attributed to Nhu Nguyen.

9 recordsLinked to original sources

arXiv2026

Stochastic Extinction with Relaxed Boundedness Conditions

We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates). While the latter is typically sharp, the former is often restrictive and can be improved. Building on the ideas initiated in \cite{benaim2018stochastic}, we develop a streamlined approach that relaxes this boundedness condition and yields concise and accessible criteria for extinction. In particular, we establish extinction criteria in two settings: with and without a linearly bounded quadratic variation condition. In the first case, our result is comparable to, and slightly improves upon, the main results in \cite{foldes2024stochastic}. In the second case, where the quadratic variation is not linearly bounded, we obtain new extinction results that fall outside the scope of existing frameworks. Several examples are provided to illustrate the applicability of our results and to highlight situations where previous conditions are not practically verifiable.

math.PR↗

arXiv2025

Optimal Meal Schedule for a Local Nonprofit Using LLM-Aided Data Extraction

We present a data-driven pipeline developed in collaboration with the Power Packs Project, a nonprofit addressing food insecurity in local communities. The system integrates data extraction from PDFs, large language models for ingredient standardization, and binary integer programming to generate a 15-week recipe schedule that minimizes projected wholesale costs while meeting nutritional constraints. All 157 recipes were mapped to a nutritional database and assigned estimated and predicted costs using historical invoice data and category-specific inflation adjustments. The model effectively handles real-world price volatility and is structured for easy updates as new recipes or cost data become available. Optimization results show that constraint-based selection yields nutritionally balanced and cost-efficient plans under uncertainty. To facilitate real-time decision-making, we deployed a searchable web platform that integrates analytical models into daily operations by enabling staff to explore recipes by ingredient, category, or through an optimized meal plan.

cs.CY↗

arXiv2025

Dynamics of stochastic microorganism flocculation models

In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes multiple layers of stochasticity, from small Brownian fluctuations, to possibly large changes due to environmental `shifts'. We are able to give a full classification of the asymptotic behavior of these models. New techniques had to be developed to prove the persistence and extinction of the process as the system is not in Kolmogorov form and, as a result, the analysis is significantly more involved.

math.PR↗

arXiv2022

Stochastic epidemic SIR models with hidden states

This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the Beddington-DeAngelis incidence rate, and a Holling type II functional response. Given that many diseases can lead to asymptomatic infections, we look at a system of stochastic differential equations that also includes a class of hidden state individuals, for which the infection status is unknown. We assume that the direct observation of the percentage of hidden state individuals that are infected, $\alpha(t)$, is not given and only a noise-corrupted observation process is available. Using the nonlinear filtering techniques in conjunction with an invasion type analysis (or analysis using Lyapunov exponents from the dynamical system point of view), this paper proves that the long-term behavior of the disease is governed by a threshold $\lambda\in \mathbb{R}$ that depends on the model parameters. It turns out that if $\lambda<0$ the number $I(t)$ of infected individuals converges to zero exponentially fast, or the extinction happens. In contrast, if $\lambda>0$, the infection is endemic and the system is permanent. We showcase our results by applying them in specific illuminating examples. Numerical simulations are also given to illustrate our results.

math.PR↗

arXiv2021

Random switching in an ecosystem with two prey and one predator

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this system is well known. However, nature is usually not deterministic. All ecosystems experience some type of random environmental fluctuations. We incorporate these into a natural framework as follows. Suppose the environment has two possible states. In each of the two environmental states the dynamics is governed by a system of Lotka-Volterra ODE. The randomness comes from spending an exponential amount of time in each environmental state and then switching to the other one. We show how this random switching can create very interesting phenomena. In some cases the randomness can facilitate the coexistence of the three species even though coexistence is impossible in each of the two environmental states. In other cases, even though there is coexistence in each of the two environmental states, switching can lead to the loss of one or more species. We look into how predators and environmental fluctuations can mediate coexistence among competing species.

math.PR↗

arXiv2021

Maximum Likelihood Estimation of Diffusions by Continuous Time Markov Chain

In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the diffusion process. Unlike typical time discretization approaches, such as psuedo-likelihood approximations with Shoji-Ozaki or Kessler's method, the CTMC approximation introduces no time-discretization error during parameter estimation, and is thus well-suited for typical econometric situations with infrequently sampled data. Due to the structure of the CTMC, we are able to obtain closed-form approximations for the sample likelihood which hold for general univariate diffusions. Comparisons of the state-discretization approach with approximate MLE (time-discretization) and Exact MLE (when applicable) demonstrate favorable performance of the CMTC estimator. Simulated examples are provided in addition to real data experiments with FX rates and constant maturity interest rates.

stat.ME↗

arXiv2021

Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples including Markov decision process, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning. Some numerical demonstrations are also provided.

math.PR↗

arXiv2021

Stability and Stabilization of Coupled Jump Diffusions and Applications

This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other subsystems (components). This paper derives sufficient conditions under which the underlying coupled jump diffusion is stable. The results are then applied to investigate the stability of linearizable jump diffusions, fast-slow coupled jump diffusions. Moreover, weak stabilization of interacting systems and consensus of leader-following systems are examined.

math.PR↗

arXiv2020

General Nonlinear Stochastic Systems Motivated by Chemostat Models: Complete Characterization of Long-Time Behavior, Optimal Controls, and Applications to Wastewater Treatment

The paper considers a chemostat model describing an activated sludge process in wastewater treatment. The model is assumed to be subject to environment noise in terms of both white noise and color noise. The paper fully characterizes the asymptotic behavior of the model that is a hybrid switching diffusion. We show that the long-term properties of the system can be classified using a value $λ$. More precisely, if $λ\leq 0$, the bacteria in the sewage will die out, which means that the process does not operate. If $λ>0$, the system has an invariant probability measure to which the transition probability of the solution process converges exponentially fast. One of the distinctive contributions of this paper is that the critical case $λ=0$ is considered. Numerical examples are given to illustrate our results.

math.PR↗