Research Statement - Carleton University
Research Statement - Carleton University
Research Statement - Carleton University
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[9] D. Dawson, and J. Vaillancourt, Stochastic McKean-Vlasov equations. NoDEA Nonlinear Differential<br />
Equations Appl. 2 (1995), 199–229.<br />
[10] G. M. Erickson, Differential game models of advertising competition, European J. Oper. Res., 83 (1995),<br />
431–438.<br />
[11] S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, J. Wiley, New York,<br />
NY, 1986.<br />
[12] D. Fudenberg and D.K. Levine, The Theory of Learning in Games, MIT Press, Cambridge, MA, 1998.<br />
[13] J. Gärtner, On the McKean-Vlasov limit for interacting diffusions, Math. Nachr., 137 (1988), 197–248.<br />
[14] I. Gyöngy, A note on Euler’s approximation, Potential Anal., 8 (1998), 205–216.<br />
[15] P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, New York,<br />
1980.<br />
[16] J.A. Heunis, Strong invariance principle for singular diffusions, Stochastic Process. Appl., 104 (2003),<br />
57–80.<br />
[17] T. Hida and M. Hitsuda. Gaussian Processes, AMS, Providence, RI, 1993.<br />
[18] M. Huang. Large-population LQG games involving a major player: the Nash certainty equivalence<br />
principle. SIAM J. Control Optim., 48 (2010), 3318–3353.<br />
[19] M. Huang, P.E. Caines, and R. P. Malhame, Individual and mass behaviour in large population stochastic<br />
wireless power control problems: Centralized and Nash equilibrium solutions, in Proc. 42nd IEEE<br />
Conf. Dec. Contr., Maui, HI, 2003, 98–103.<br />
[20] M. Huang, P. E. Caines and R. P. Malhamé. Large-population cost-coupled LQG problems with nonuniform<br />
agents: Individual-mass behavior and decentralized ϵ-Nash equilibria. IEEE Trans. Autom. Control,<br />
52 (2007), 1560–1571.<br />
[21] H. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time,<br />
Springer-Verlag, 2001.<br />
[22] V.E. Lambson, Self-enforcing collusion in large dynamic markets, J. Econ. Theory, 34 (1984), 282–291.<br />
[23] J.-M. Lasry and P.-L. Lions. Jeux à champ moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris,<br />
343 (2006), 619–625.<br />
[24] J.-M. Lasry and P.-L. Lions. Jeux à champ moyen. II. Horizon fini et contrle optimal, C. R. Math.<br />
Acad. Sci. Paris, 343 (2006), 679–684.<br />
[25] J.-M. Lasry and P.-L. Lions. Mean field games, Japan. J. Math., 2 (2007), 229–260.<br />
[26] T. Li and J.-F. Zhang. Asymptotically optimal decentralized control for large population stochastic<br />
multiagent systems, IEEE Trans. Automat. Control, 53 (2008), 1643–1660.<br />
[27] J. Kiefer, On the deviations in the Skorokhod-Strassen approximation scheme, Z. Wahrsch. Verw.<br />
Gebiete, 13 (1969), 321–332.<br />
[28] P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag,<br />
1992.<br />
[29] X. Mao, A. Truman, and C. Yuan, Euler-Maruyama approximations in mean-reverting stochastic<br />
volatility model under regime-switching, J. Appl. Math. Stoch. Anal., (2006), Article ID 80967.<br />
[30] M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990.<br />
[31] G.N. Milstein and M.V. Tretyakov, Stochastic Numerics for Mathematical Physics, Springer-Verlag,<br />
Berlin, 2004.<br />
[32] S.L. Nguyen and M. Huang, LQG Mixed games with continuum-parametrized minor players, (2011),<br />
submitted.<br />
[33] S.L. Nguyen and G. Yin, Asymptotic properties of hybrid random processes modulated by Markov<br />
chains, to appear in Nonlinear Analysis: Theory, Methods and Applications, 71 (2009), e1638–e1648.<br />
[34] S.L. Nguyen and G. Yin, Asymptotic properties of Markov modulated random sequences with fast and<br />
slow time scales, Stochastics, 82 (2010), 445–474.<br />
[35] S.L. Nguyen and G. Yin, Weak convergence of Markov modulated random sequences, Stochastics, 82<br />
(2010), 521–552.<br />
[36] S.L. Nguyen and G. Yin, Pathwise convergence rate for numerical solutions of stochastic differential<br />
equations, IMA Journal of Numerical Analysis, (2011), in press, doi: 10.1093/imanum/drr025.<br />
[37] S.L. Nguyen and G. Yin, Pathwise convergence rate for numerical solutions of Markovian switching<br />
stochastic differential equations, Nonlinear Analysis: Real World Applications, (2011), to appear.<br />
[38] S.P. Sethi and Q. Zhang, Hierarichical Decision Making in Stochastic Manufacturing Systems,<br />
Birkhäuser, Boston, 1994.<br />
[39] H.A. Simon and A. Ando, Aggregation of variables in dynamic systems, Econometrica, 29 (1961),<br />
111–138.<br />
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