Research interests: 

1. Applied Mathematics, Probability and Applied Probability: 

   1. • Mathematical Biology

      • Mathematical Physics

      • Stochastic Optimization and its Application

      • Large Deviations and Moderate Deviations Theory and its Applications

      • Stability and Stabilization of Stochastic Systems

      • Stochastic processes and stochastic equations

2. Statistics

My research is in part supported by the National Science Foundation under the grant DMS 2407669.

Publications:

[34.] Analysis of Reaction-Diffusion Predator-Prey System under Random Switching (with N. Du), Nonlinear Analysis: Hybrid Systems, to appear. [arXiv]

[33.] Some Applications of New Results in Stochastic Approximation with Discontinuous Drifts (with Q. Le, G. Yin), 2025 11th International Conference on Control, Decision and Information Technologies (CoDIT).

[32.] Pymle: A python package for maximum likelihood estimation and simulation of stochastic differential equations (with H. Chau, J. Kirkby, D. Nguyen, Duy Nguyen, T. Nguyen), Journal of Statistical Software, to appear.

[31.] Longtime behavior of impulsive stochastic vegetation ecosystem with jump-diffusion, (with T. Tuong, D. Nguyen), Numerical Algebra, Control and Optimization, Vol 14 (2024), 795-812. [Journal][pdf]

[30.] On The Inversion-free Newton’s Method And Its Applications (with H. Chau, J. Kirkby, D. Nguyen, Duy Nguyen, T. Nguyen), International Statistical Review, Vol. 92 (2024), 284–321. [Journal][pdf]

[29.] An Efficient method to Simulate Diffusion Bridges (with H. Chau, J. Kirkby, D. Nguyen, Duy Nguyen, T. Nguyen), Statistics and Computing, Vol. 34 (2024), 131. [Journal][pdf]

[28.] Second-Order Fast-Slow Stochastic Systems (with G. Yin),  SIAM Journal on Mathematical Analysis, Vol. 56 (2024), 5175–5208. [Journal] [arXiv]

[27.] Hybrid stochastic SIS epidemic models with vaccination: stability of the disease-free state and applications (with T. Hieu, D. Nguyen, T. Tuong), Nonlinear Analysis: Hybrid Systems, Vol. 53 (2024), 101492. [Journal] [pdf]

[26.]  Stability of Stochastic Functional Differential Equations with Past-Dependent Random Switching Involving Countably Infinite States (with D. Nguyen, T. Trang, G. Yin), IEEE Transactions on Automatic Control,  Vol. 69 (2024), 1612-1626. [Journal] [pdf]

[25.] Analyzing a class of stochastic SIRS models under imperfect vaccination (with N. Hieu, D. Nguyen, G. Yin), Journal of the Franklin Institute, Vol. 361 (2024), 1284-1302. [Journal] [pdf]

[24.] Stochastic Multi-group Epidemic SVIR Models: Degenerate Case (with D. Nguyen, T. Tuong),  Communications in Nonlinear Science and Numerical Simulation, Vol. 128 (2024), 107588. [Journal] [pdf]

[23.] Stability and Stabilization of Coupled Jump Diffusions and Applications (with D. Nguyen, Duy Nguyen, G. Yin), Journal of Differential Equations, Vol 379 (2024), 175-206. [Journal] [arXiv]

[22.] Stochastic nutrient-plankton models (with A. Hening, N. Hieu, D. Nguyen),  Journal of Differential Equations, Vol. 376 (2023), 370-405. [Journal] [arXiv]

[21.] A stochastic epidemic SIR model with hidden states (with N. Du, A. Hening, G. Yin), Nonlinear Analysis: Hybrid Systems, Vol. 49 (2023), 101368. [Journal] [arXiv]

[20.] Stochastic Approximation with Discontinuous Dynamics, Differential Inclusions, and Applications (with G. Yin), Annals of Applied Probability, Vol. 33 (2023), 780–823. [Journal] [arXiv] 

[19.] Random switching in an ecosystem with two prey and one predator (with A. Hening, D. Nguyen, H. Watts), SIAM Journal on Mathematical Analysis, Vol 55 (2023), 347-366.  [Journal] [arXiv]

[18.] Exponential tightness of a family of Skorohod integrals, Electronic Communications in Probability, Vol. 27 (2022), paper no. 1, 1-14. [Journal] [arXiv] 

[17.] Maximum likelihood estimation of diffusion using continuous time Markov chain (with J. Kirkby, D. Nguyen, Duy Nguyen), Computational Statistics and Data Analysis, Vol. 168 (2022), 107408. [Journal] [arXiv]

[16.] Inversion-free Subsampling Newtons Method For Large Sample Logistic Regression (with J. Kirkby, D. Nguyen, Duy Nguyen), Statistical Papers,  Vol. 63 (2022), 943-963. [Journal] [pdf]

[15.] Stochastic Functional Kolmogorov Equations I: Persistence (with D. Nguyen, G. Yin), Stochastic Processes and their Applications, Vol. 142 (2021), 319-364. [Journal] [arXiv]

[14.] Stochastic Functional Kolmogorov Equations II: Extinction (with D. Nguyen, G. Yin), Journal of Differential Equations, Vol. 294 (2021), 1-39. [Journal] [arXiv]

[13.] Large Deviations Principles for Langevin Equations in Random Environment and Applications (with G. Yin), Journal of Mathematical Physics, Vol. 62 (2021), 083301. [Journal] [arXiv]

[12.] Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis (with G. Yin), Journal of Differential Equations, Vol. 282 (2021), 184-232.  [Journal] [arXiv]

[11.] Stability of Stochastic Functional Differential Equations with Random Switching and Applications (with N. Du, D. Nguyen, G. Yin), Automatica, Vol. 125 (2021), 109410. [Journal] [pdf]

[10.] Characterization of long-term behavior of stochastic NP ecological model under regime switching (with T. Tuong), Communications in Nonlinear Science and Numerical Simulation, Vol. 93 (2021), 105497. [Journal] [pdf]

[9.] Longtime behavior of a class of stochastic tumor-immune systems (with T. Tuong, G. Yin), Systems & Control Letters, Vol. 146 (2020), 104806. [Journal] [pdf]

[8.] Permanence and Extinction for the Stochastic SIR Epidemic Model (with N. Du), Journal of Differential Equations, Vol. 269 (2020), 9619-9652. [Journal] [arXiv]

[7.] General Nonlinear Stochastic Systems Motivated by Chemostat Models: Complete Characterization of Long-Time Behavior, Optimal Controls, and Applications to Wastewater Treatment (with D. Nguyen, G. Yin), Stochastic Processes and their Applications, Vol. 130 (2020), 4608-4642. [Journal] [arXiv]

[6.] A Class of Langevin Equations with Markov Switching Involving Strong Damping and Fast Switching (with G. Yin), Journal of Mathematical Physics, Vol. 61 (2020), 063301. [Journal] [pdf]

[5.] Analysis of A Spatially Inhomogeneous Stochastic Partial Differential Equation Epidemic Model (with D. Nguyen, G. Yin), Journal of Applied Probability, Vol. 57 (2020), 613-636. [Journal] [arXiv]

[4.] Stochastic Partial Differential Equation Models for Spatially Dependent Predator-Prey Equations (with G. Yin), Discrete and Continuous Dynamical Systems-Series B, Vol. 25 (2020), 117-139. [Journal] [arXiv]

[3.] Stochastic Partial Differential Equation SIS Epidemic Models: Modeling and Analysis (with G. Yin), Communication on Stochastic Analysis, Vol. 13 (2019). [Journal] [pdf]

[2.] Conditions for Permanence and Ergodicity of Certain SIR Epidemic Models (with N. Dieu, N. Du), Acta Applicandae Mathematicae, Vol. 160 (2019), 81-99. [Journal] [pdf]

[1.] Permanence and extinction of certain stochastic SIR models perturbed by a complex type of noises (with N. Du), Applied Mathematics Letters, Vol. 64 (2017), 223-230. [Journal] [pdf]