Free Access
Volume 27, 2021
Article Number 6
Number of page(s) 34
Published online 04 March 2021
  1. O. Alvarez and M. Bardi, Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40 (2002) 1159–1188. [Google Scholar]
  2. O. Alvarez and M. Bardi, Singular perturbations of nonlinear degenerate parabolic PDEs: a general convergence result. Arch. Ration. Mech. Anal. 170 (2003) 17–61. [Google Scholar]
  3. O. Alvarez and M. Bardi, Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Mem. Amer. Math. Soc. 204 (2010) 1–88. [Google Scholar]
  4. M. Arisawa and P.-L. Lions, On ergodic stochastic control. Commun. Partial Differ. Equ. 23 (1998) 2187–2217. [Google Scholar]
  5. M. Bardi and A. Cesaroni, Optimal control with random parameters: a multiscale approach. Eur. J. Control 17 (2011) 30–45. [Google Scholar]
  6. M. Bardi, A. Cesaroni and L. Manca, Convergence by viscosity methods in multiscale financial models with stochastic volatility. SIAM J. Financial Math. 1 (2010) 230–65. [Google Scholar]
  7. A. Bensoussan, Perturbation methods in optimal control. Translated from the French by C. Tomson. Wiley/Gauthier-Villars Series in Modern Applied Mathematics. John Wiley & Sons, Ltd., Chichester; Gauthier-Villars, Montrouge (1988). [Google Scholar]
  8. V.S. Borkar and K. Suresh Kumar Singular perturbations in risk-sensitive stochastic control. SIAM J. Control Optim. 48 (2010) 3675–3697. [Google Scholar]
  9. V.S. Borkar and V. Gaitsgory, Singular perturbations in ergodic control of diffusions. SIAM J. Control Optim. 46 (2007) 1562–1577. [Google Scholar]
  10. M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27 (1992) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  11. M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations in infinite dimensions. IV. Hamiltonians with unbounded linear terms. J. Funct. Anal. 90 (1990) 237–283. [Google Scholar]
  12. G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions. Second edition. Encyclopedia of Mathematics and its Applications, 152. Cambridge University Press, Cambridge (2014). [Google Scholar]
  13. T.D. Donchev and A.L. Dontchev, Singular perturbations in infinite-dimensional control systems. SIAM J. Control Optim. 42 (2003) 1795–1812. [Google Scholar]
  14. G. Fabbri, F. Gozzi and A. Święch, Stochastic optimal control in infinite dimension. Dynamic programming and HJB equations. With a contribution by Marco Fuhrman and Gianmario Tessitore. Probability Theory and Stochastic Modelling, 82. Springer, Cham (2017). [Google Scholar]
  15. D. Ghilli, Viscosity methods for large deviations estimates of multiscale stochastic processes. ESAIM: COCV 24 (2018) 605–637. [CrossRef] [EDP Sciences] [Google Scholar]
  16. G. Guatteri and G. Tessitore, Singular limit of BSDEs and optimal control of two scale stochastic systems in infinite dimensional spaces. To appear in: Appl. Math. Optim. (2019) [Google Scholar]
  17. Y. Kabanov and S. Pergamenshchikov, Two-scale stochastic systems. Asymptotic analysis and control. Applications of Mathematics (New York), 49. Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2003). [Google Scholar]
  18. Y. Kabanov and W.J. Runggaldier, On control of two-scale stochastic systems with linear dynamics in the fast variables. Math. Control Signals Syst. 9 (1996) 107–122. [Google Scholar]
  19. D. Kelome and A. Święch, Perron’s method and the method of relaxed limits for “unbounded” PDE in Hilbert spaces. Studia Math. 176 (2006) 249–277. [Google Scholar]
  20. H.J. Kushner, Weak convergence methods and singularly perturbed stochastic control and filtering problems. Systems & Control: Foundations & Applications, 3. Birkhäuser Boston, Inc., Boston, MA (1990). [Google Scholar]
  21. P.-L. Lions, Une inégalité pour les opérateurs elliptiques du second ordre. Ann. Mat. Pura Appl. 127 (1981) 1–11. [Google Scholar]
  22. P. Mannucci, C. Marchi and N. Tchou, Singular perturbations for a subelliptic operator. ESAIM: COCV 24 (2018) 1429–1451. [EDP Sciences] [Google Scholar]
  23. D.S. Naidu, Singular perturbations and time scales in control theory and applications: an overview. Singularly perturbed dynamic systems in control technology. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algor. 9 (2002) 233–278. [Google Scholar]
  24. K. Suresh Kumar Singular perturbations in stochastic ergodic control problems. SIAM J. Control Optim. 50 (2012) 3203–3223. [Google Scholar]
  25. J.T.F. Yang, Singular perturbation of stochastic control and differential games. Ph.D. thesis, The University of Sydney (2020). [Google Scholar]
  26. Y. Zhang, D.S. Naidu, C. Cai and Y. Zou, Singular perturbations and time scales in control theories and applications: an overview 2002–2012. Int. J. Inf. Syst. Sci. 9 (2014) 1–36. [Google Scholar]

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