University of Puerto Rico    (787) 764 0000

    Professor Information

    Son Luu Nguyen

    Address Department of Mathematics, 17 University Ave. Ste 1701
    San Juan PR, 00925-2537
    Office NCN II C-124
    Hours Contact: sonluu.nguyen@upr.edu
    Actual Program
    Telephone (787) 764-0000 88277
    E-Mail

    Education

    PhD, Wayne State University, 2010

    Research Interests

    Limit Theorems in Probability and Stochastic Processes, Numerical Solution of Stochastic Differential Equations, Stochastic Games and Stochastic Optimal Control, Stochastic Approximation and Recursive Algorithms, Mathematical Finance.

    Selected Publications

    1. D.H. Nguyen, D. Nguyen, and S.L. Nguyen, Stability in distribution of path-dependent hybrid diffusion. SIAM Journal on Control and Optimization (to appear).
    2. D.T. Nguyen, S.L. Nguyen, and N.H. Du, Convergence in Monge-Wasserstein distance of mean field systems with locally Lipschitz coefficients.Acta Mathematica Vietnamica. (in press).
    3. G. Yin and S.L. Nguyen. Switching diffusions with mean-field interactions: Limit results, maximum principle, and non-Markov systems, in Stochastic Modeling and Control, Eds. J. Jakubowski, M. Nieweglowski, M. Rasonyi and L. Stettner, Banach Center Publications. (in press).
    4. V.A. Bokil, N.L. Gibson, S.L. Nguyen, E.A. Thomann, and E.C. Waymire, An Euler-Maruyama method for diffusion equations with discontinuous coefficients and a family of interface conditions. Journal of Computational and Applied Mathematics, 368 ( 2020), 112545.
    5. S.L. Nguyen, D.T. Nguyen, and G. Yin, A stochastic maximum principle for switching diffusions using conditional mean fields with applications to control problems. ESAIM: Control, Optimisation, and Calculus of Variations, 26 (2020) article 69.
    6. S.L. Nguyen, G. Yin, and T.A. Hoang, On laws of large numbers for systems with mean-field interactions and Markovian switching. Stochastic Processes and their Applications, 130 (2020), no.1, 262-296.
    7. D.T. Nguyen, S.L. Nguyen, and N.H. Du, On mean field systems with multi-classes. Discrete and Continuous Dynamical Systems. Series A, 40 (2020), no.2, 683-707.
    8. D.T. Nguyen and S.L. Nguyen, Euler-Maruyama method for regime switching stochastic differential equations with Holder coefficients. Communications on Stochastic Analysis, 13 (2019), no.3, article 4.
    9. D.T. Nguyen, S.L. Nguyen, T.A. Hoang, and G. Yin, Tamed-Euler method for hybrid stochastic differential equations with Markovian switching. Nonlinear Analysis: Hybrid Systems, 30 (2018), 14-30.
    10. S.L. Nguyen, T.A. Hoang, D.T. Nguyen and G. Yin, Milstein-type procedures for numerical solutions of stochastic differential equations with Markovian switching. SIAM Journal on Numerical Analysis, 55 (2017), no.2, 953–979.
    11. M. Huang and S.L. Nguyen, Mean field games for stochastic growth with relative utility, Applied Mathematics and Optimization, 74 (2016), no.3, 643–668.
    12. T.A. Hoang, S.L. Nguyen and G. Yin, Nearly optimal and nearly equilibrium controls with wide band-width noise for hybrid systems, Dynamics of Continuous, Discrete & Impulsive Systems. Series A: Mathematical Analysis, 23 (2016), no.3, 163–194.
    13. S.L. Nguyen and M. Huang, LQG mixed games with continuum-parametrized minor players, SIAM Journal on Control and Optimization, 50 (2012), no.5, 2907-2937.
    14. S.L. Nguyen and G. Yin, Pathwise convergence rates for numerical solutions of Markovian switching stochastic differential equations, Nonlinear Analysis: Real World Applications, 13 (2012), 1170-1185.
    15. S.L. Nguyen and G. Yin, Pathwise convergence rate for numerical solutions of stochastic differential equations, IMA Journal of Numerical Analysis, 32 (2012), 701-723.
    16. S.L. Nguyen and G. Yin, Weak convergence of Markov modulated random sequences, Stochastics, 82 (2010), no.6, 521-552.
    17. S.L. Nguyen and G. Yin, Asymptotic properties of Markov modulated random sequences with fast and slow time scales, Stochastics, 82 (2010), no.5, 445-474.

    Grants and Awards

    1. Outstanding Research Award, Department of Mathematics, Wayne State University, April 2009.
    2. Andre G. Laurent Award in Recognition of Outstanding Achievement in the Ph.D. Program, Department of Mathematics, Wayne State University, April 2010.

    Additional Information

    Scholarship:

    1. The Karl W. and Helen L. Folley Endowed Mathematics Scholarship, Department of Mathematics, Wayne State University, April 2008.
    2. The Thomas C. Rumble Fellowship, Department of Mathematics, Wayne State University, August 2005, May 2006.


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