Free Access
Issue |
ESAIM: COCV
Volume 14, Number 2, April-June 2008
|
|
---|---|---|
Page(s) | 343 - 355 | |
DOI | https://doi.org/10.1051/cocv:2007053 | |
Published online | 20 March 2008 |
- S. Aida, S. Kusuoka and D. Stroock, On the support of Wiener functionals, Asymptotic problems in probability theory: Wiener functionals and asymptotics (Sanda/Kyoto, 1990), Pitman Res. Notes Math. Ser 284, Longman Sci. Tech., Harlow (1993) 3–34. [Google Scholar]
- J.-P. Aubin and G. Da Prato, The viability theorem for stochastic differential inclusions. Stochastic Anal. Appl 16 (1998) 1–15. [CrossRef] [MathSciNet] [Google Scholar]
- J.-P. Aubin and H. Doss, Characterization of stochastic viability of any nonsmooth set involving its generalized contingent curvature. Stochastic Anal. Appl 21 (2003) 955–981. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkäuser, Boston (1997). [Google Scholar]
- M. Bardi and A. Cesaroni, Almost sure stabilizability of controlled degenerate diffusions. SIAM J. Control Optim 44 (2005) 75–98. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bardi and F. Da Lio, Propagation of maxima and strong maximum principle for viscosity solution of degenerate elliptic equations. I: Convex operators. Nonlinear Anal 44 (2001) 991–1006. [Google Scholar]
- M. Bardi and F. Da Lio, Propagation of maxima and strong maximum principle for fully nonlinear degenerate elliptic equations. II: Concave operators. Indiana Univ. Math. J 52 (2003) 607–627. [Google Scholar]
- M. Bardi and P. Goatin, Invariant sets for controlled degenerate diffusions: a viscosity solutions approach, in Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, W.M. McEneaney, G.G. Yin and Q. Zhang Eds., Birkhäuser, Boston (1999) 191–208. [Google Scholar]
- M. Bardi and R. Jensen, A geometric characterization of viable sets for controlled degenerate diffusions. Set-Valued Anal 10 (2002) 129–141. [Google Scholar]
- T. Başar and P. Bernhard, H∞-optimal control and related minimax design problems. A dynamic game approach, 2nd edn., Birkhäuser, Boston (1995). [Google Scholar]
- G. Ben Arous, M. Grădinaru and M. Ledoux, Hölder norms and the support theorem for diffusions. Ann. Inst. H. Poincaré Probab. Statist 30 (1994) 415–436. [MathSciNet] [Google Scholar]
- P. Bernhard, Robust control approach to option pricing, including transaction costs, in Advances in dynamic games, Ann. Internat. Soc. Dynam. Games 7, Birkhäuser, Boston (2005) 391–416. [Google Scholar]
- 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. [Google Scholar]
- P. Cardaliaguet, A differential game with two players and one target. SIAM J. Control Optim 34 (1996) 1441–1460. [CrossRef] [MathSciNet] [Google Scholar]
- A. Cesaroni, Stability properties of controlled diffusion processes via viscosity methods. Ph.D. thesis, University of Padova (2004). [Google Scholar]
- A. Cesaroni, A converse Lyapunov theorem for almost sure stabilizability. Systems Control Lett 55 (2006) 992–998. [CrossRef] [MathSciNet] [Google Scholar]
- M.C. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc 27 (1992) 1–67. [Google Scholar]
- G. Da Prato and H. Frankowska, Invariance of stochastic control systems with deterministic arguments. J. Diff. Equ 200 (2004) 18–52. [CrossRef] [Google Scholar]
- H. Doss, Liens entre équations différentielles stochastiques et ordinaires. Ann. Inst. H. Poincaré Sect. B (N.S.) 13 (1977) 99–125. [MathSciNet] [Google Scholar]
- W.H. Fleming and H.M. Soner, Controlled Markov Process and Viscosity Solutions. Springer-Verlag, New York (1993). [Google Scholar]
- R.A. Freeman and P.V. Kokotovic: Robust nonlinear control design. State-space and Lyapunov techniques. Birkäuser, Boston (1996). [Google Scholar]
- U.G. Haussmann and J.P. Lepeltier, On the existence of optimal controls. SIAM J. Control Optim 28 (1990) 851–902. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Lin, E.D. Sontag, Control-Lyapunov universal formulas for restricted inputs. Control Theory Adv. Tech 10 (1995) 1981–2004. [MathSciNet] [Google Scholar]
- A. Millet and M. Sanz-Solé, A simple proof of the support theorem for diffusion processes, Séminaire de Probabilités, XXVIII, Lect. Notes Math 1583, Springer, Berlin (1994) 36–48. [Google Scholar]
- G.J. Olsder, Differential game-theoretic thoughts on option pricing and transaction costs. Int. Game Theory Rev 2 (2000) 209–228. [CrossRef] [MathSciNet] [Google Scholar]
- H.M. Soner and N. Touzi, Dynamic programming for stochastic target problems and geometric flow. J. Eur. Math. Soc 4 (2002) 201–236. [CrossRef] [MathSciNet] [Google Scholar]
- H.M. Soner and N. Touzi, A stochastic representation for the level set equations. Comm. Part. Diff. Equ 27 (2002) 2031–2053. [CrossRef] [Google Scholar]
- P. Soravia, Pursuit-evasion problems and viscosity solutions of Isaacs equations. SIAM J. Control. Optim 31 (1993) 604–623. [Google Scholar]
- P. Soravia, Stability of dynamical systems with competitive controls: the degenerate case. J. Math. Anal. Appl 191 (1995) 428–449. [CrossRef] [MathSciNet] [Google Scholar]
-
P. Soravia,
control of nonlinear systems: differential games and viscosity solutions. SIAM J. Control Optim 34 (1996) 1071–1097. [CrossRef] [MathSciNet] [Google Scholar]
-
P. Soravia, Equivalence between nonlinear
control problems and existence of viscosity solutions of Hamilton-Jacobi-Isaacs equations. Appl. Math. Optim 39 (1999) 17–32. [Google Scholar]
- D.W. Stroock and S.R.S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley (1972) 333–359. [Google Scholar]
- D.W. Stroock and S.R.S. Varadhan, On degenerate elliptic-parabolic operators of second order and their associated diffusions. Comm. Pure Appl. Math 25 (1972) 651–713. [CrossRef] [MathSciNet] [Google Scholar]
- H.J. Sussmann, On the gap between deterministic and stochastic ordinary differential equations. Ann. Probability 6 (1978) 19–41. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.