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Applied Mathematics and Statistics

Faculty

Ky Q. Tran img
Ky Q. Tran
  • PositionAssociate Professor
  • OfficeB 525
  • Phone032-626-1911
  • Emailky.tran@stonybrook.edu

Ky Q. Tran, Associate Professor

  • B.A. in Mathematics Education and B.S. in Mathematical Analysis, Hue University, Vietnam,
  • M.A. in Mathematical Statistics and Ph.D. in Applied Mathematics, 2016, Wayne State University, USA
  • Research Interests: Applied Probability

After earning his Ph.D., Dr. Tran worked as a Mathematics Lecturer at Hue University in Vietnam and as a Norbert Wiener Assistant Professor at Tufts University. He joined SUNY Korea in Spring 2019.

His research interests mainly focus on the areas of stochastic systems, stochastic control, applied probability, mathematical biology, numerical algorithms, and their applications. 

He has taught a variety of courses, including Precalculus (MAT123), Applied Calculus 1 (AMS151), Applied Linear Algebra (AMS210), Applied Calculus III (AMS261), Survey of Probability and Statistics (AMS310), Probability (AMS311), Financial Mathematics (AMS318), and Probability Theory (AMS507).

My primary research interests lie in the domains of Stochastic Systems, Stochastic Control, Applied Probability, Stochastic Processes, and Numerical Methods. My focus is on the development and analysis of stochastic hybrid systems, which may include jumps, various delays, and impulses. My objective is to establish explicit criteria for different types of stability and to address stabilization challenges. Additionally, I am dedicated to creating numerical approximations for these complex systems. Building upon this foundation, I explore numerous related optimal control problems. A significant part of my work involves the development of numerical methods to approximate both the cost (or value) function and optimal controls, utilizing the Markov chain approximation method.

Fields of Interest
Stochastic Systems, Stochastic Control,  Applied Probability and Stochastic Processes, Mathematical Biology, and Numerical Algorithms

Research Website

Publications

  1. Tran, K., & Yin, G. (2013). Asymptotic expansions of solutions for parabolic systems associ- ated with transient switching diffusions. Applicable Analysis, 93(6), 1239–1255. https://doi.org/10.1080/00036811.2013.825255

  2. Tran, K., & Yin, G. (2014). Hybrid competitive Lotka–Volterra ecosystems with a hidden Markov chain. Journal of Control and Decision, 1(1), 51–74. https://doi.org/10.1080/23307706.2014.885291

  3. Tran, K., & Yin, G. (2014). Stochastic competitive Lotka–Volterra ecosystems under partial observation: Feedback Controls for permanence and extinction. Journal of the Franklin Insti- tute, 351(8), 4039–4064.
    https://doi.org/10.1016/j.jfranklin.2014.04.015

  4. Tran, K., & Yin, G. (2015). Optimal harvesting strategies for stochastic competitive Lotka–Volterra ecosystems. Automatica, 55, 236–246.
    https://doi.org/10.1016/j.automatica.2015.03.017

  5. Tran,K., Yin, G., Wang, L. Y., & Zhang, H. (2016). Singularly perturbed multi-scale switching diffusions. Dynamic Systems and Applications, 25 (2016), 153–173.

  6. Tran, K., Yin, G., & Wang, L. Y. (2016). A generalized Goodwin Business Cycle Model in Random Environment. Journal of Mathematical Analysis and Applications, 438(1), 311–327. https://doi.org/10.1016/j.jmaa.2016.02.006

  7. Tran, K., & Yin, G. (2016). Numerical methods for optimal harvesting strategies in random environments under partial observations. Automatica, 70, 74–85. https://doi.org/10.1016/j.automatica.2016.03.025

  8. Tran, K., & Yin, G. (2017). Asymptotic expansions for solutions of parabolic systems as- sociated with multi-scale switching diffusions. Acta Mathematicae Applicatae Sinica, English Series, 33(3), 731–752.
    https://doi.org/10.1007/s10255-017-0695-9

  9. Tran, K. Q., & Yin, G. (2017). Optimal harvesting strategies for stochastic ecosystems. IET Control Theory & Applications, 11(15), 2521–2530. https://doi.org/10.1049/iet-cta.2016.1621

  10. Chen, X., Chen, Z.-Q., Tran, K., & Yin, G. (2017). Recurrence and ergodicity for a class of regime-switching jump diffusions. Applied Mathematics & Optimization, 80(2), 415–445. https://doi.org/10.1007/s00245-017-9470-9

  11. Chen, X., Chen, Z.-Q., Tran, K., & Yin, G. (2019). Properties of switching jump diffusions: Maximum principles and Harnack inequalities. Bernoulli, 25(2). https://doi.org/10.3150/17-bej1012

  12. Du, N.H., Dieu, N.T., Tran, K., & Sam, V.H. (2020). Long-time behavior of a stochastic SIQR model with Markov switching. Acta Mathematica Vietnamica. 45(4), 903–915. https://doi.org/10.1007/s40306-020-00376-0

  13. Hening, A., Tran, K. Q., Phan, T. T., & Yin, G. (2019). Harvesting of interacting stochastic populations. Journal of Mathematical Biology, 79(2), 533–570. https://doi.org/10.1007/s00285-019-01368-x

  14. Tuong, T. D., Nguyen, D. H., Dieu, N. T., & Tran, K. (2019). Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate. Nonlinear Analysis: Hybrid Systems, 34, 121–130.
    https://doi.org/10.1016/j.nahs.2019.05.008

  15. Hening, A., & Tran, K. Q. (2020). Harvesting and seeding of stochastic populations: Analysis and numerical approximation. Journal of Mathematical Biology, 81(1), 65–112. SCIE. https://doi.org/10.1007/s00285-020-01502-0

  16. Tran, K. (2021). Optimal exploitation for hybrid systems of renewable resources under partial observation. Nonlinear Analysis: Hybrid Systems, 40, 101013. https://doi.org/10.1016/j.nahs.2021.101013

  17. Tran, K., & Yin, G. (2021). Optimal Control and Numerical Methods for hybrid stochastic SIS models. Nonlinear Analysis: Hybrid Systems, 41, 101051. https://doi.org/10.1016/j.nahs.2021.101051

  18. Tran, K. Q. (2021). Exponential contraction of switching jump diffusions with a hidden Markov chain. Statistics & Probability Letters, 178, 109191. https://doi.org/10.1016/j.spl.2021.109191

  19. Tran, K. Q., & Tien, P. T. (2021). Explicit criteria for moment exponential stability and instability of switching diffusions with L ́evy noise. International Journal of Control, 95(12), 3298–3308. SCIE.
    https://doi.org/10.1080/00207179.2021.1971301

  20. Jin, Z., Tran, K., & Yin, G. (2022). Numerical Solutions of stochastic control problems: Markov chain approximation methods. Numerical Control: Part A, 233–264 (in Handbook of Numerical Analysis, Vol 23: Numerical Control, E. Tr ́elat and E. Zuazua Eds, Elsevier). https://doi.org/10.1016/bs.hna.2021.12.007

  21. Jin, Z., Qiu, M., Tran, K. Q., & Yin, G. (2022). A survey of numerical solutions for stochastic control problems: Some recent progress. Numerical Algebra, Control & Optimization, 12(2), 213.
    https://doi.org/10.3934/naco.2022004

  22. Tran, K. Q., & Nguyen, D. H. (2022). Exponential stability of impulsive stochastic differential equations with Markovian switching. Systems & Control Letters, 162, 105178. https://doi.org/10.1016/j.sysconle.2022.105178

  23. Hening, A., Tran, K. Q., & Ungureanu, S. C. (2022). The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking. Journal of Mathematical Biol- ogy, 84(6).
    https://doi.org/10.1007/s00285-022-01750-2

  24. Tran, K. Q., & Le, B. T. N. (2022). On exponential stability of non-autonomous stochastic differential equations with Markovian switching. Statistics & Probability Letters, 189, 109602. https://doi.org/10.1016/j.spl.2022.109602

  25. Ngoc, P. H., & Tran, K. Q. (2022). On stability of solutions of stochastic delay differential equations. Systems & Control Letters, 169, 105384. https://doi.org/10.1016/j.sysconle.2022.105384

  26. Tran, K. Q., Nguyen, D. H., & Yin, G. (2022). Stability in distribution and stabilization of switching jump diffusions. ESAIM: Control, Optimisation and Calculus of Variations, 28, 72. https://doi.org/10.1051/cocv/2022062

  27. Tran, K. Q., Le, B. T., & Yin, G. (2022). Harvesting of a stochastic population under a mixed regular-singular control formulation. Journal of Optimization Theory and Applications, 195(3), 1106–1132.
    https://doi.org/10.1007/s10957-022-02127-7

  28. Tran, K. Q., & Yin, G. (2023). Exponential stability of stochastic functional differential equations with impulsive perturbations and Markovian switching. Systems & Control Letters, 173, 105457.
    https://doi.org/10.1016/j.sysconle.2023.105457

  29. Anh Ngoc, P. H., & Tran, K. Q. (2023). On stability of numerical solutions of neutral stochastic delay differential equations with time-dependent delay. Mathematical Methods in the Applied Sciences.
    https://doi.org/10.1002/mma.9179

  30. Ngoc, P.H.A., Nguyen, L.S., & Tran, K. Q. (2023). On exponential contraction and expansion of Markovian switching diffusions. International Journal of Control. https://doi.org/10.1080/00207179.2023.2201645

  31. Tran, K. Q., & Yin, G. (2023). Numerical Solutions of Stochastic Functional Differential Equations with Impulsive Perturbations and Markovian Switching. Nonlinear Analysis: Hybrid Systems, 50, 101409.
    https://doi.org/10.1016/j.nahs.2023.101409

 

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