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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 42 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 42
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2025030
Published online 14 May 2025
  1. M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems. Vol. 260 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 3rd edn. Springer, Heidelberg (2012). Translated from the 1979 Russian original by Joseph Szücs. [Google Scholar]
  2. Yu.M. Kabanov and S.M. Pergamenshchikov, On optimal control of singularly perturbed stochastic differential Equations, in Modeling, estimation and control of systems with uncertainty (Sopron, 1990). Vol. 10 of Progr. Systems Control Theory. Birkhäuser Boston, Boston, MA (1991). [Google Scholar]
  3. M. Bardi and H. Kouhkouh, Singular perturbations in stochastic optimal control with unbounded data. ESAIM Control Optim. Calc. Var. 29 (2023) Paper No. 52, 25. [CrossRef] [EDP Sciences] [Google Scholar]
  4. S. Assing, F. Flandoli and U. Pappalettera, Stochastic model reduction: convergence and applications to climate equations. J. Evol. Equ. 21 (2021) 3813–3848. [CrossRef] [MathSciNet] [Google Scholar]
  5. É. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, in Stochastic partial differential equations and their applications (Charlotte, NC, 1991). Vol. 176 of Lect. Notes Control Inf. Sci.. Springer, Berlin (1992) 200–217. [Google Scholar]
  6. G. Fabbri, F. Gozzi and A. Swiech, Stochastic optimal control in infinite dimension. Vol. 82 of Probability Theory and Stochastic Modelling. Springer, Cham (2017). Dynamic programming and HJB equations, With a contribution by Marco Fuhrman and Gianmario Tessitore. [Google Scholar]
  7. Yu.M. 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. [CrossRef] [Google Scholar]
  8. O. Alvarez and M. Bardi, Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40 (2001) 1159–1188. [Google Scholar]
  9. 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]
  10. O. Alvarez, M. Bardi and C. Marchi, Multiscale problems and homogenization for second-order Hamilton–Jacobi equations. J. Differ. Equ. 243 (2007) 349–387. [CrossRef] [Google Scholar]
  11. M. Bardi and A. Cesaroni, Optimal control with random parameters: a multiscale approach. Eur. J. Control 17 (2011) 30–45. [Google Scholar]
  12. M. Bardi, A. Cesaroni and L. Manca, Convergence by viscosity methods in multiscale financial models with stochastic volatility. SIAM J. Financial Math. 1 (2010) 230–265. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Guatteri and G. Tessitore, Singular limit of BSDEs and optimal control of two scale stochastic systems in infinite dimensional spaces. Appl. Math. Optim. 83 (2021) 1025–1051. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Fuhrman, Y. Hu and G. Tessitore, Ergodic BSDES and optimal ergodic control in Banach spaces. SIAM J. Control Optim. 48 (2009) 1542–1566. [CrossRef] [MathSciNet] [Google Scholar]
  15. P.Y. Madec, Y. Hu and A. Richou, A probabilistic approach to large time behavior of mild solutions of HJB equations in infinite dimension. SIAM J. Control Optim. 53 (2015) 378–398. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Guatteri and G. Tessitore, Ergodic BSDEs with multiplicative and degenerate noise. SIAM J. Control Optim. 58 (2020) 2050–2077. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Swiech, Singular perturbations and optimal control of stochastic systems in infinite dimension: HJB equations and viscosity solutions. ESAIM Control Optim. Calc. Var. 27 (2021) Paper No. 6, 34. [CrossRef] [EDP Sciences] [Google Scholar]
  18. C.-E. Bréhier, Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component. Stochastic Process. Appl. 130 (2020) 3325–3368. [CrossRef] [MathSciNet] [Google Scholar]
  19. C.-E. Bréehier, Strong and weak orders in averaging for SPDEs. Stochastic Process. Appl. 122 (2012) 2553–2593. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Röckner and L. Xie, Averaging principle and normal deviations for multiscale stochastic systems. Commun. Math. Phys. 383 (2021) 1889–1937. [CrossRef] [Google Scholar]
  21. F. De Feo, The order of convergence in the averaging principle for slow-fast systems of stochastic evolution equations in Hilbert spaces. Appl. Math. Optim. 88 (2023) 1–36. [CrossRef] [Google Scholar]
  22. A. Święch and J. Zabczyk, Uniqueness for integro-PDE in Hilbert spaces. Potential Anal. 38 (2013) 233–259. [CrossRef] [MathSciNet] [Google Scholar]
  23. A. Święch and J. Zabczyk, Integro-PDE in Hilbert spaces: existence of viscosity solutions. Potential Anal. 45 (2016) 703–736. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Święch, “Unbounded” second order partial differential equations in infinite-dimensional Hilbert spaces. Commun. Part. Differ. Equ. 19 (1994) 1999–2036. [Google Scholar]
  25. G. Barles, R. Buckdahn and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations. Stoch. Rep. 60 (1997) 57–83. [CrossRef] [Google Scholar]
  26. R. Carbone, B. Ferrario and M. Santacroce, Backward stochastic differential equations driven by càdlàg martingales. Theory Probab. Appl. 52 (2008) 304–314. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Confortola, M. Fuhrman and J. Jacod, Backward stochastic differential equations driven by a marked point process: an elementary approach, with an application to optimal control. Ann. Appl. Probab. 26 (2016) 1743–1773. [CrossRef] [MathSciNet] [Google Scholar]
  28. E. Bandini, Existence and uniqueness for backward stochastic differential equations driven by a random measure, possibly non quasi-left continuous. Electron. Commun. Probab. 20 (2015) 1–13. [CrossRef] [MathSciNet] [Google Scholar]
  29. E. Bandini, F. Confortola and A. Cosso, BSDE representation and randomized dynamic programming principle for stochastic control problems of infinite-dimensional jump-diffusions. Electron. J. Probab. 24 (2019) 1–37. [CrossRef] [Google Scholar]
  30. S. Peszat and J. Zabczyk, Stochastic partial differential equations with L´evy noise. Vol, 113 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2007). [Google Scholar]
  31. G. Da Prato and J. Zabczyk, Ergodicity for infinite-dimensional systems. Vol. 229 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (1996). [Google Scholar]
  32. M. Fuhrman and G. Tessitore, Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control. Ann. Probab. 30 (2002) 1397–1465. [Google Scholar]
  33. F. Confortola and M. Fuhrman, Filtering of continuous-time Markov chains with noise-free observation and applications. Stochastics 85 (2013) 216–251. [CrossRef] [MathSciNet] [Google Scholar]
  34. S.N. Cohen and V. Fedyashov, Ergodic BSDEs with jumps and time dependence. Preprint arXiv:1406.4329v2 (2015). [Google Scholar]
  35. S.N. Cohen and R.J. Elliott, Stochastic calculus and applications. Probability and its Applications, 2nd edn. Springer, Cham (2015). [Google Scholar]
  36. G. Guatteri and G. Tessitore, Singular limit of two-scale stochastic optimal control problems in infinite dimensions by vanishing noise regularization. SIAM J. Control Optim. 60 (2022) 575–596. [CrossRef] [MathSciNet] [Google Scholar]
  37. J.-P. Aubin and H. Frankowska, Set-valued analysis. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA (2009). Reprint of the 1990 edition. [CrossRef] [Google Scholar]

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