Stochastic Invariance for Differential Inclusions

Set-Valued Analysis

Volumn 8, Issue 1-2, 2000, Pages 181-201

  Aubin, Jean Pierre ^a   Da Prato, Giuseppe ^a   Frankowska, Hélène ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Stochastic differential inclusions; Stochastic invariance; Viability

Indexed keywords

EID: 0034562449     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008738928302     Document Type: Article

References (54)

1. Aubin, J.-P.: Viability Theory, Birkhäuser, Boston, 1991.
2. Aubin, J.-P. and Da Prato, G.: Stochastic viability and invariance, Ann. Scuola Norm. Sup. Pisa 27 (1990), 595-694.
3. Aubin, J.-P. and Da Prato, G.: Stochastic Nagumo's viability theorem, Stochastic Anal. Appl. 13 (1995), 1-11.
4. Aubin, J.-P. and Da Prato, G.: The viability theorem for stochastic differential inclusions, Stochastic Anal. Appl. 16(1998), 1-15.
5. Aubin, J.-P. and Dordan, O.: Fuzzy control systems and toll sets, in: Hung Nguyen (ed.), Handbook of Fuzzy Systems, 1996.
6. Aubin, J.-P. and Frankowska, H.: Set-Valued Analysis, Birkhäuser, Boston, 1990.
7. Bardi, M. and Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston, 1997.
8. Bardi, M. and Goatin, P.: A Dirichlet type problem for nonlinear degenerate elliptic equations arinsing in time-optimal stochastic control, Preprint SISSA 50/97, 1997.
9. Bardi, M. and Goatin, P.: Invariant sets for controlled degenerate diffusions: A viscosity solution approach, Preprint Padova 2/98, 1998.
10. Bensoussan, A.: Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam, 1982.
11. Bjork, T. and Christensen, B. J.: Interest rates dynamics and cnsstent forward rate curves, Preprint, 1997.
12. Bjork, T. and Gombani, A.: Minimal realizations of forward rates, Preprint, Stockolm, 1997.
13. Bjork, T., Di Masi, G., Kabanov, Yu. and Runggaldier, W.: Towards a general theory of bond markets, Preprint, 1999.
14. Bjork, T. and Swensson, L.: On the existence of finite dimensional realizations for nonlinear forward rate models, Preprint, 1999.
15. Brace, A., Gatarek, D. and Musiela, M.: The market model of interest rate dynamics, Math. Finance 7 (1997), 127-154.
16. Brace, A. and Musiela, M.: A multifactor Gauss Markov implementation of heath, Jarrow and Morton, Math. Finance 4 (1994), 259-283.
17. Bouchaud, J.-P., Cont, R., El Karoui, N., Potters, M. and Sagna, N.: Phenomenology of the interest rate curve: A statistical analysis of the term structure deformations, Preprint, 1997.
18. Buckdahn, R., Quincampoix, M. and Rascanu, A.: Propriétés de viabilité pour des équations différentielles stochastiques rétrogrades et applications à des équations aux dérivées partielles, C.R. Acad. Sci. 235 (1997), 1159-1162.
19. Buckdahn, R., Quincampoix, M. and Rascanu, A.: Stochastic viability for backward stochastic differential equations and applications to partial differential equations, Univ. Bretagne Occidentale, 01-1998, 1998.
20. Buckdahn, R., Peng, S., Quincampoix, M. and Rainer, C.: Existence of stochastic control under state constraints, C.R. Acad. Sci. 327 (1998), 17-22.
21. Da Prato, G.: Introduction to Differential Stochastic Equations, Appunti dei corsi, Scuola Normale di Pisa, 1995.
22. Da Prato, G.: Stochastic Evolution Equations by Semi-Group Methods, Centre de Recerca Matematica, 1995.
23. Da Prato and Frankowska, H.: A stochastic Filippov theorem, Stochastic Calculus 12 (1994), 409-426.
24. Da Prato, G. and Zabczyk, J.: A Note on Semilinear Stochastic Equations, Scuola Normale Superiore, Pisa, 1987.
25. Da Prato, G. and Zabczyk, J.: Stochastic Evolution Equations in Infinite Dimensions, Cambridge Univ. Press, 1992.
26. Da Prato, G. and Zabczyk, J.: Ergodicity for Infinite Dimensional Systems, Cambridge Univ. Press, 1996.
27. Filipovic, D.: Invariant manifolds for weak solutions to stochastic equations, Preprint, 1999.
28. Frankowska, H. and Rampazzo, F.: Filippov's and Filippov-Wazewski's theorems in the presence of state constraints, J. Differential Equations (to appear).
29. Gatarek, D.: Some remarks on the market model of interest rates, Control Cybernet. 25 (1996), 1233-1244.
30. Gautier, S. and Thibault, L.: Viability for constrained stochastic differential equations, Differential Integral Equations 6 (1993), 1395-1414.
31. Ikeda, N. and Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
32. Jachimiak, W.: A note on invariance for semilinear differential equations, Bull. Pol. Acad. Sci. 44 (1996), 179-183.
33. Jachimiak, W.: Stochastic invariance in infinite dimension, Preprint, 1998.
34. Jensen, R. R.: Uniqueness of viscosity solutions of 2nd order elliptic partial differential equations, 1999.
35. Milian, A.: A note on the stochastic Invariance for Itô equations, Bull. Polish Acad. Sci. 41 (1993), 139-150.
36. Milian, A.: On multi-dimensional difusion process living in a bounded region, Stochastic Anal. Appl. 11 (1993).
37. m, 1994.
38. Milian, A.: Stochastic viability and a comparison theorem, Colloq. Math. 68 (1995), 297-316.
39. Milian, A.: Invariance for stochastic equations with regular coefficients, Stochastic Anal. Appl. 15 (1997), 91-101.
40. Milian, A.: Comparison theorems for stochastic evolution equations, Preprint, 1998.
41. Musiela, M.: Stochastic PDE's and term stucture models, IGR-AFFI, La Baule, 1993.
42. Musiela, M. and Rutkowski, M.: Martingale Methods in Finance and Modelling, Springer, New York, 1997.
43. Nagumo, M.: Uber die lage derintegralkurven gewhnlicher differentialgleichungen, Proc. Phys. Math. Soc. Japan 24 (1942), 551-559.
44. Neveu, J.: Bases mathématiques du cacul des probabilités, Masson, Paris, 1964.
45. Strook, D. W. and Varadhan, S. R. S.: On the support of diffusion processes with applications to the strong maximum principle, Proc. Sixth Berkeley Sympos. Mathematical Statistics and Probability, Vol. 111. Probability Theory, Univ. of California Press, 1972, pp. 333-359.
46. Stroock, D. W. and Varadhan, S. R. S.: Multidimensional Diffusion Processes, Springer, New York, 1979.
47. Tessitore, G. and Zabczyk, J.: Comments on transition semi-groups and stochastic invariance, Preprint, 1998.
48. Zabczyk, J.: Exit problem for infinite dimensional systems, in: Proc. Workshop on Stochastic PDE's and Applications, 1985.
49. Zabczyk, J.: Some comments on stabilizability, J. Appl. Math. Optim. (1985).
50. Zabczyk, J.: Law equivalence of Ornstein-Uhlenbeck processes and control equivalence of linear systems, Institute of Mathematics Polish Academy of Sciences, Reprint 457, 1989.
51. Zabczyk, J.: Mathematical Control Theory: An Introduction, Birkhäuser, Basel, 1992.
52. Zabczyk, J.: Chance and Decision: Stochastic Control in Discrete Time, Quaderni, Scuola Normale di Pisa, 1996.
53. Zabczyk, J.: Stable dynamical systems under small perturbations, J. Math. Anal. Appl. (to appear).
54. Zabczyk, J.: Stochastic invariance and consistency of financial models, Preprint Scuola Normale di Pisa, 1999.