Part of my research is supported by National Science Foundation under the NSF Grant DMS # 2407669.

Research interests:

Applied Probability, Stochastic Processes, Optimal Control, Dynamical Systems, Mathematical Biology, Stochastic Optimization, Statistics.

Publications:

  1. (with Chau HN, Kirkby JL, Nguyen D, Nguyen NN, Nguyen T), On the Inversion‐Free Newton’s Method and Its Applications, International Statistical Review. 92(2024) no. 2, 284-321.
  2. (with Ky Q. Tran, Tran D. Tuong,  George Yin), A class of long-run average control problems of Lotka-Voltera systems in a stochastic environment, Mathematical Control and Related Fields (2023).
  3. (with Tuong, Tran D.,  Nhu N. Nguyen), Longtime behavior of impulsive stochastic vegetation ecosystem with jump-diffusion, Numerical Algebra, Control and Optimization (2024).
  4. (with Hieu, Nguyen T., Nhu N. Nguyen, Tran D. Tuong), Hybrid stochastic SIS epidemic models with vaccination: Stability of the disease-free state and applications, Nonlinear Analysis: Hybrid Systems 53 (2024): 101492.
  5. (with N. Hieu, N. Nguyen, G. Yin), Stochastic multi-group epidemic SVIR models: Degenerate case, Analyzing a class of stochastic SIRS models under imperfect vaccination Journal of the Franklin Institute, 361(2024) no. 3, 1284-1302
  6. (with D. Nguyen, N. Nguyen, G. Yin), Stability of coupled jump diffusions and applications,  J. Differential Equations. 379 (2024),  175-206
  7. (with N. Nguyen, T. Ta, G. Yin), Stability of Stochastic Functional Differential Equations with Past-Dependent Random Switching Involving Countably Infinite States, IEEE Trans. Automat. Control, 2024
  8. (with N. Nguyen, T. Tuong), Stochastic multi-group epidemic SVIR models: Degenerate case, Commun. Nonlinear Sci. Numer. Simul.  (2024)
  9. (with A. Hening, N. Hieu, N. Nguyen)  Stochastic nutrient-plankton models, J. Differential Equations. 376(2023), 370-405
  10. (with A. Hening, N. Nguyen, H. Watts) Random switching in an ecosystem with two prey and one predator. SIAM J. Math. Anal. 55 (2023), no. 1, 347–366
  11. (with A. Hening, S. Schreiber) Coevolution of Patch Selection in Stochastic Environments. The American Naturalist, 202 (2023), no 2, 122-139.
  12. (with K. Tran, G. Yin), Stability in distribution and stabilization of switching jump diffusions. ESAIM Control Optim. Calc. Var. 28 (2022), Paper No. 72, 26 pp.
  13. (with K. Tran) Exponential stability of impulsive stochastic differential equations with Markovian switching, Systems Control Lett. 162 (2022), 105178. ​
  14. (with M. Benaim and A. Bourquin) Stochastic persistence in degenerate stochastic Lotka-Volterra food chains, Discrete Contin. Dyn. Syst. Ser. B, (2022).
  15. (with J. Kirkby, D. Nguyen and N. Nguyen) Maximum likelihood estimation of diffusions using continuous time Markov chain,   Comput. Statist. Data Anal. 168, April 2022, 107408.
  16. (with J. Kirby, N. Nguyen, D. Nguyen) Inversion-free subsampling Newton’s method for large sample logistic regression, Statist. Papers. 
  17. (with M.N. Tran, D. Nguyen) Variational Bayes on manifolds, Stat. Comput.  31(2021) Paper No. 71 
  18. (with N. Nguyen, G. Yin) Stochastic functional Kolmogorov  equations I: persistence, Stochastic Process. Appl.  142 (2021), 319-364.
  19. (with N. Nguyen, G. Yin) Stochastic functional Kolmogorov  equations II: extinction, J. Differential Equations. 294 (2021), 1-39.
  20. (with T.A. Phan, J. P. Tian) Deterministic and stochastic modeling for PDGF-driven gliomas reveals a classification of gliomas. J. Math. Biol. 83 (2021), no. 2, Paper No. 22.
  21. (with A. Hening, S. Schreiber),  A classification of the dynamics of three-dimensional stochastic ecological systems, Ann. Appl. Probab. (to appear).
  22. (with P. Chesson, A. Hening) A general theory of coexistence and extinction for stochastic ecological communities, J. Math. Biol.  82 (2021), no. 6, Paper No. 56.
  23. (with N. Du, A. Hening and G. Yin)  Dynamical systems with fast switching and slow diffusion: Hyperbolic equilibria and stable limit cycles,  J. Differential Equations. 293, 25 August 2021, Pages 313-358.
  24. (with N. Du, N. Nguyen, G. Yin)  Stability of stochastic functional differential equations with random switching and applications, Automatica, 125 (2021), 109410.
  25. (with S.L. Nguyen, D. Nguyen)  Stability in Distribution of Path-Dependent Hybrid Diffusion, SIAM J. Control Optim., 59 (2021), no. 1, 434–463. 
  26. (with H. Watts, A. Mishra, T. D. Tuong) Dynamics of a vector-host model under switching environments, Discrete Contin. Dyn. Syst. Ser. B, 22(2021)
  27. (with J. Kirby, D. Nguyen)  A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions, Appl. Math. Comput., 386 (2020),  no.1, 125472.
  28. (with E. Strickler) A method to deal with the critical case in stochastic population dynamics, SIAM J. Appl. Math.  80(2020), 1567–1589.
  29. (with G. Yin, C. Zhu) Long-term Analysis of A Stochastic SIRS Model with General Incidence Rates, SIAM J. Appl. Math. 80(2020), no. 2,  814–838 (pdf)
  30. (with N. Nguyen, G. Yin) Analysis of A Spatially Inhomogeneous Stochastic Partial Differential Equation Epidemic Model, J. Appl. Probab.  57(2020), no. 2, 613-636.
  31. (with N. Nguyen, G. Yin) General nonlinear stochastic systems motivated by chemostat models: Complete characterization of long-time behavior, optimal controls, and applications to wastewater treatment,  Stochastic Process. Appl.  130(2020), no. 8, 4608-4642 (pdf)
  32. (with A. Hening) The competitive exclusion principle in stochastic environments, J. Math. Biol.  80(2020),1323-1351(pdf) 
  33. (with G. Yin) Stability of Stochastic Functional Differential Equations with Regime-Switching: Analysis Using Dupire’s Functional Itô Formula, Potential Anal.  53 (2020), 247–265 (pdf) 
  34. (with T. Tuong, N. Dieu, K. Tran) Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate, Nonlinear Anal. Hybrid Syst. 34 (2019),121-130.
  35. (with G. Yin) Stability of Regime-Switching Diffusion Systems with Discrete States Belonging to a Countable Set,  SIAM J. Control Optim. 56(2018) no 5, 3893-3917. (pdf)
  36. (with A. Hening) Coexistence and extinction for stochastic Kolmogorov systems, Ann. Appl. Probab. 28 (2018), no.(3) 1893-1942, (pdf) 
  37. (with A. Hening, S. C. Ungureanu and T. K. Wong) Asymptotic harvesting of populations in fluctuating environments, to appear in J. Math. Biol (pdf)
  38. (with G. Yin)  Sustainable Harvesting Policies Under Long-Run Average Criteria: Near Optimality, to appear in Appl. Math. Optim  81(2020),​ 443–478. (pdf)
  39. (with G. Yin) Recurrence for linearizable switching diffusion with past dependent switching and countable state space,  Math. Control Relat. Fields  8(2018) no.(3&4): 879-897. (pdf)
  40. (with A. Hening) Persistence in stochastic Lotka-Volterra food chains with intraspecific competition,  Bull. Math. Biol. 80 (2018), No 10, 2527–2560 (pdf)
  41. (with A. Hening) Stochastic Lotka-Volterra food chains, J. Math. Biol (2018) 77:135–163 (pdf)
  42. (with A. Hening and G. Yin) Stochastic population growth in spatially heterogeneous environments: The density-dependent case, J. Math. Biol 76 (2018), No. 3, 697–754. (pdf)
  43. (with G.Yin) Recurrence and Ergodicity of Switching Diffusions with Past-Dependent Switching Having A Countable State Space, Potential Anal. 48 (2018), no. 4, 405–435. (pdf)
  44. (with G. Yin and C. Zhu) Certain Properties Related to Well Posedness of Switching Diffusions, Stochastic Process. Appl. 127 (2017), No 10 3135-3158 (pdf).
  45. (with G. Yin) Switching diffusion with past dependent switching and countable switching space: Existence and uniqueness of solutions, recurrence, and weak stabilization.Decision and Control (CDC), IEEE 56th Annual Conference on. IEEE (2017) 1858-1863.
  46. (with G. Yin) Coexistence and Exclusion of Stochastic Competitive Lotka-Volterra Models, J. Differential Equations. 262 (2017), no. 3, 1192-1225. (pdf)
  47. (with G. Yin) Modeling and Analysis of Switching Diffusion Systems: Past-Dependent Switching Having a Countable State Space and Related Control System Models, SIAM J. Control Optim.  54 (2016), no. 5, 2450-2477. (pdf)
  48. (with N. Dieu, N. Du and G. Yin) Classification of Asymptotic Behavior in A Stochastic SIR Model, SIAM J. Appl. Dyn. Syst. 15 (2016), no. 2, 1062-1084. (pdf)
  49. (with N. Dieu, N. Du and G. Yin) Protection Zones for Survival of Species in Random Environment, SIAM J. Appl. Math.  76 (2016), no. 4, 1382-1402. (Preprint version)
  50. (with N. Du and G. Yin) Conditions for permanence and ergodicity of certain stochastic predator-prey models,  J. Appl. Probab. 53 (2016), 187-202. (pdf) (Notes)
  51. (with N. Du and G. Yin) Study of Certain Stochastic Predator-Prey Models, SIAM Conf.  Control Appl., (2015) 408-415. (pdf)
  52. (with N. Du and G. Yin) Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise. J. Differential Equations 257 (2014), no. 6, 2078-2101. (pdf)
  53. (with N. Du) Asymptotic behavior of Kolmogorov systems with predator-prey type in random environment. Commun. Pure Appl. Anal. 13 (2014), no. 6, 2693-2712. (pdf)
  54. (with P. Auger, N. Du, N. Hieu), Dynamical behavior of a stochastic sirs epidemic model, Math. Model. Nat. Phenom. 10 (no. 2, 2015), (pdf) 
  55. (with N. Du, N. Dieu) On stability in distribution of stochastic differential delay equations with Markovian switching.  Systems Control Lett. 65 (2014), 43-49. (pdf)
  56. A note on sufficient conditions for asymptotic stability in distribution of stochastic differential equations with Markovian switching. Nonlinear Anal. 95 (2014), 625-631. (pdf)
  57. (with H. Tuan and V. Khu) Dynamics of a stochastic predator-prey model with Beddington DeAngelis functional response. Sci. Ser. A Math. Sci. (N.S.) 22 (2012), 75-84. (pdf)
  58. (with T. Lan), Exponential stability of nontrivial solutions of stochastic differential equations. Sci. Ser. A Math. Sci. (N.S.) 21 (2011), 97-106. (pdf)
  59. (with N. Du, T. Ta), Asymptotic behavior of predator-prey systems perturbed by white noise. Acta Appl. Math. 115 (2011), no. 3, 351-370. (pdf)
  60. (with N. Du), Dynamics of Kolmogorov systems of competitive type under the telegraph noise. J. Differential Equations 250 (2011), no. 1, 386-409. (pdf)​

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