Free Access
Issue
ESAIM: COCV
Volume 18, Number 2, April-June 2012
Page(s) 401 - 426
DOI https://doi.org/10.1051/cocv/2010103
Published online 13 April 2011
  1. O. Alvarez and A. Tourin, Viscosity solutions of nonlinear integro-differential equations. Ann. Inst. Henri Poincaré, Anal. non linéaire 13 (1996) 293-317.
  2. J.-P. Aubin, Viability Theory. Birkhäuser (1992).
  3. J.-P. Aubin and G. Da Prato, Stochastic viability and invariance. Ann. Sc. Norm. Pisa 27 (1990) 595–694.
  4. J.-P. Aubin and H. Frankowska, Set Valued Analysis. Birkhäuser (1990).
  5. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations. Systems and Control : Foundations and Applications, Birkhäuser (1997).
  6. M. Bardi and P. Goatin, Invariant sets for controlled degenerate diffusions : a viscosity solutions approach, in Stochastic analysis, control, optimization and applications, Systems Control Found. Appl., Birkhäuser, Boston, MA (1999) 191–208.
  7. M. Bardi and R. Jensen, A geometric characterization of viable sets for controlled degenerate diffusions. Set-Valued Anal. 10 (2002) 129–141. [CrossRef] [MathSciNet]
  8. G. Barles and C. Imbert, Second-order elliptic integro-differential equations : Viscosity solutions theory revisited. Ann. Inst. Henri Poincaré, Anal. non linéaire 25 (2008) 567–585. [CrossRef]
  9. G. Barles and E.R. Jakobsen, On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations. ESAIM : M2AN 36 (2002) 33–54. [CrossRef] [EDP Sciences]
  10. R. Buckdahn, S. Peng, M. Quincampoix and C. Rainer, Existence of stochastic control under state constraints. C. R. Acad. Sci. Paris Sér. I Math. 327 (1998) 17–22. [CrossRef] [MathSciNet]
  11. R. Buckdahn, D. Goreac and M. Quincampoix, Stochastic optimal control and linear programming approach. Appl. Math. Opt. 63 (2011) 257–276. [CrossRef] [MathSciNet]
  12. D.L. Cook, A.N. Gerber and S.J. Tapscott, Modelling stochastic gene expression : Implications for haploinsufficiency. Proc. Natl. Acad. Sci. USA 95 (1998) 15641–15646. [CrossRef]
  13. A. Crudu, A. Debussche and O. Radulescu, Hybrid stochastic simplifications for multiscale gene networks. BMC Systems Biology 3 (2009).
  14. M.H.A. Davis, Markov Models and Optimization, Monographs on Statistics and Applied probability 49. Chapman & Hall (1993).
  15. M. Delbrück, Statistical fluctuations in autocatalytic reactions. J. Chem. Phys. 8 (1940) 120–124. [CrossRef]
  16. S. Gautier and L. Thibault, Viability for constrained stochastic differential equations. Differential Integral Equations 6 (1993) 1395–1414. [MathSciNet]
  17. J. Hasty, J. Pradines, M. Dolnik and J.J. Collins, Noise-based switches and amplifiers for gene expression. PNAS 97 (2000) 2075–2080. [CrossRef] [PubMed]
  18. H.M. Soner, Optimal control with state-space constraint. II. SIAM J. Control Optim. 24 (1986) 1110–1122. [CrossRef] [MathSciNet]
  19. X. Zhu and S. Peng, The viability property of controlled jump diffusion processes. Acta Math. Sinica 24 (2008) 1351–1368. [CrossRef]

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