Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control, SIAM Journal on Control and Optimization, vol.40, issue.4, pp.1159-1188, 2001. ,
DOI : 10.1137/S0363012900366741
Singular Perturbations of Nonlinear Degenerate Parabolic PDEs: a General Convergence Result, Archive for Rational Mechanics and Analysis, vol.170, issue.1, pp.17-61, 2003. ,
DOI : 10.1007/s00205-003-0266-5
Bardi: Ergodicity, stabilization, and singular perturbations for Bellman- Isaacs equations, Mem. Amer, Math. Soc, vol.204, issue.960, 2010. ,
DOI : 10.1090/s0065-9266-09-00588-2
Multiscale problems and homogenization for second-order Hamilton???Jacobi equations, Journal of Differential Equations, vol.243, issue.2, pp.349-387, 2007. ,
DOI : 10.1016/j.jde.2007.05.027
URL : http://doi.org/10.1016/j.jde.2007.05.027
Multiscale singular perturbations and homogenization of optimal control problems, in Geometric control and nonsmooth analysis, Series on Advances in Mathematics for Applied Sciences, 2008. ,
Capuzzo-Dolcetta: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, 1997. ,
DOI : 10.1007/978-0-8176-4755-1
Convergence by Viscosity Methods in Multiscale Financial Models with Stochastic Volatility, SIAM Journal on Financial Mathematics, vol.1, issue.1, pp.230-265, 2010. ,
DOI : 10.1137/090748147
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.7734
On the Bellman equation for some unbounded control problems, NoDEA : Nonlinear Differential Equations and Applications, vol.4, issue.4, pp.491-510, 1997. ,
DOI : 10.1007/s000300050027
Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods, Calculus of Variations and Partial Differential Equations, vol.18, issue.2, pp.159-179, 2003. ,
DOI : 10.1007/s00526-002-0186-5
Perturbation methods in optimal control, 1988. ,
Controlled diffusions in a random medium, Stochastics, vol.241, issue.2, pp.87-120, 1988. ,
DOI : 10.1002/cpa.3160390604
Perturbation analysis of optimization problems, Springer Series in Operations Research, 2000. ,
Averaging of Singularly Perturbed Controlled Stochastic Differential Equations, Applied Mathematics and Optimization, vol.56, issue.2, pp.169-209, 2007. ,
DOI : 10.1007/s00245-007-0893-6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.9709
Singular Perturbations in Ergodic Control of Diffusions, SIAM Journal on Control and Optimization, vol.46, issue.5, pp.1562-1577, 2007. ,
DOI : 10.1137/060657327
Weak Dynamic Programming Principle for Viscosity Solutions, preprint 2009, available at HAL preprint server ,
DOI : 10.1137/090752328
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.635.432
Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media, Communications on Pure and Applied Mathematics, vol.45, issue.3, pp.319-361, 2005. ,
DOI : 10.1002/cpa.20069
Optimization?theory and applications, 1983. ,
DOI : 10.1007/978-1-4613-8165-5
Nonsmooth analysis and control theory, 1998. ,
DOI : 10.1007/978-1-4614-1806-1_69
URL : https://hal.archives-ouvertes.fr/hal-00863298
user's guide to viscosity solutions\\ of second order\\ partial
differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992. ,
DOI : 10.1090/S0273-0979-1992-00266-5
Uniqueness Results for Second-Order Bellman--Isaacs Equations under Quadratic Growth Assumptions and Applications, SIAM Journal on Control and Optimization, vol.45, issue.1, pp.74-106, 2006. ,
DOI : 10.1137/S0363012904440897
URL : https://hal.archives-ouvertes.fr/hal-00455993
Singular perturbations in control problems, Automation and Remote Control, vol.67, issue.1, pp.1-43, 2006. ,
DOI : 10.1134/S0005117906010012
Well-posed optimization problems, Lecture Notes in Mathematics, vol.1543, 1993. ,
DOI : 10.1007/BFb0084195
Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.1248, issue.3-4, pp.359-375, 1989. ,
DOI : 10.1137/0326063
Soner: Controlled Markov processes and viscosity solutions, 2006. ,
Sircar: Derivatives in financial markets with stochastic volatility, 2000. ,
Solna: Singular perturbations in option pricing, SIAM J. Appl. Math, vol.63, issue.5, pp.1648-1665, 2003. ,
Multiscale Stochastic Volatility Asymptotics, Multiscale stochastic volatility asymptotics, pp.22-42, 2003. ,
DOI : 10.1137/030600291
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.7852
Stochastic stability of differential equations, Sijthoff & Noordhoff , Alphen aan den Rijn?Germantown, 1980. ,
Uniqueness of unbounded viscosity solution of Hamilton Jacobi equations, Indiana Univ, Math. J, vol.33, issue.5, pp.721-748, 1984. ,
Some asymptotic problems in fully nonlinear elliptic equations and stochastic control, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.11, issue.4, pp.129-176, 1984. ,
Two-scale stochastic systems Asymptotic analysis and control, 2003. ,
Musiela: Ergodicity of diffusion processes, preprint, 2002. ,
Singular perturbations and time scales in control theory and applications: an overview, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, vol.9, pp.233-278, 2002. ,
DOI : 10.1109/cdc.1987.272924
Veretennikov: On the Poisson equation and diffusion approximation, I , Ann, Probab, vol.29, pp.1061-1085, 2001. ,
Veretennikov: On the Poisson equation and diffusion approximation, II , Ann. Probab, pp.31-1166, 2003. ,
Optimal control theory. Applications to management science and economics, 2000. ,
Bounds and Asymptotic Approximations for Utility Prices when Volatility is Random, SIAM Journal on Control and Optimization, vol.43, issue.4, pp.1328-1353, 2004. ,
DOI : 10.1137/S0363012903409253
Optimal control, Birkhäuser Boston, 2000. ,
URL : https://hal.archives-ouvertes.fr/inria-00629428