Skip to main content

A PDE approach to asymptotic estimates for optimal exit probabilities

  • Control Theory
  • Conference paper
  • First Online:
Stochastic Differential Systems Filtering and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 69))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. G. Crandall and P.-L. Lions, "Viscosity solutions of Hamilton-Jacobi equations", Trans. Amer. Math. Soc. 277 (1983), 1–42.

    Google Scholar 

  2. M. G. Crandall, L. C. Evans, and P.-L. Lions, "Some properties of viscosity solutions of Hamilton-Jacobi equations", Trans. Amer. Math. Soc. 282 (1984), 487–502.

    Google Scholar 

  3. M. G. Crandall, P.-L. Lions and P. E. Souganidis, in preparation.

    Google Scholar 

  4. M. G. Crandall and P. E. Souganidis, "Developments in the theory of nonlinear first-order partial differential equations", Proceedings of International Symposium on Differential Equations, Birmingham, Alabama (1983), Knowles and Lewis, eds.; North Holland.

    Google Scholar 

  5. R. J. Elliott and N. J. Kalton, "The existence of value in differential games", Memoirs Amer. Math. Soc. 126 (1972).

    Google Scholar 

  6. L. C. Evans and H. Ishii, "Nonlinear first order PDE on bounded domains", to appear.

    Google Scholar 

  7. L. C. Evans and H. Ishii, "A PDE approach to some asymptotic problems concerning random differential equations with small noise parameters", to appear.

    Google Scholar 

  8. L. C. Evans and P. E. Souganidis, "Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations", to appear in Indiana Univ. Math. Journal.

    Google Scholar 

  9. W. H. Fleming, "Stochastic control for small noise intensities", SIAM J. Control 9 (1971), 473–517.

    Google Scholar 

  10. W. H. Fleming, "Exit probabilities and optimal stochastic control", Appl. Math. Optim. 7 (1978), 329–346.

    Google Scholar 

  11. W. H. Fleming and C.-P. Tsai, "Optimal exit probabilities and differential games", Appl. Math. Optim. 7 (1981), 253–282.

    Google Scholar 

  12. P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Pitman, 1982.

    Google Scholar 

  13. P.-L. Lions and P. E. Souganidis, "Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Isaacs' equations", to appear in SIAM Journal of Control and Optimization.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. Metivier E. Pardoux

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Fleming, W.H., Souganidis, P.E. (1985). A PDE approach to asymptotic estimates for optimal exit probabilities. In: Metivier, M., Pardoux, E. (eds) Stochastic Differential Systems Filtering and Control. Lecture Notes in Control and Information Sciences, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005083

Download citation

  • DOI: https://doi.org/10.1007/BFb0005083

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15176-0

  • Online ISBN: 978-3-540-39253-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics