5 citations · 22 across the 13 of their papers we have counts for
15 papers
Stochastic nutrient-plankton models
Alexandru Hening, Nguyen Trong Hieu, Dang Hai Nguyen +1
We analyze plankton-nutrient food chain models composed of phytoplankton, herbivorous zooplankton and a limiting nutrient. These models have played a key role in understanding the…
Stochastic epidemic SIR models with hidden states
Nguyen Du, Alexandru Hening, Nhu Nguyen +1
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 liter…
Second-Order Fast-Slow Stochastic Systems
Nhu N. Nguyen, George Yin
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statis…
Random switching in an ecosystem with two prey and one predator
Alexandru Hening, Dang Nguyen, Nhu Nguyen +1
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 (…
Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications
Nhu Nguyen, George Yin
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the us…
Maximum Likelihood Estimation of Diffusions by Continuous Time Markov Chain
J. L. Kirkby, Dang Nguyen, Duy Nguyen +1
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 a…
Stability and Stabilization of Coupled Jump Diffusions and Applications
Dang Nguyen, Duy Nguyen, Nhu Nguyen +1
This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (c…
Stochastic Functional Kolmogorov Equations II: Extinction
Dang H. Nguyen, Nhu N. Nguyen, George Yin
This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equation…
Stochastic Functional Kolmogorov Equations (I): Persistence
Dang H. Nguyen, Nhu N. Nguyen, George Yin
This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differenti…
Large Deviations Principles for Langevin Equations in Random Environment and Applications
Nhu N. Nguyen, George Yin
In contrast to the study of Langevin equations in a homogeneous environment in the literature, the study on Langevin equations in randomly-varying environments is relatively scarce…
Exponential tightness of a family of Skorohod integrals
Nhu N. Nguyen
Exponential tightness of a family of Skorohod integrals is studied in this paper. We first provide a counterexample to illustrate that in general the exponential tightness with spe…
Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis
N. N. Nguyen, G. Yin
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contras…
Stochastic Partial Differential Equation Models for Spatially Dependent Predator-Prey Equations
N. N. Nhu, G. Yin
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs)…
Analysis of A Spatially Inhomogeneous Stochastic Partial Differential Equation Epidemic Model
Dang H Nguyen, Nhu N Nguyen, George Yin
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epid…
General Nonlinear Stochastic Systems Motivated by Chemostat Models: Complete Characterization of Long-Time Behavior, Optimal Controls, and Applications to Wastewater Treatment
Dang H. Nguyen, Nhu Nguyen, George Yin
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…