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.

Selected Publications: (Click here for the full list of publications.)

• 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, Vol. 113 (4) (2025), 1–40. [Journal]

• 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]

• 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]

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

• 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]

• 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]

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

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

• 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]

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

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

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

• 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]

• 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]

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

• 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]