Applied Mathematics and Optimization

, Volume 9, Issue 1, pp 177–191

Integro-differential operators associated with diffusion processes with jumps

  • Suzanne Lenhart
Article

Abstract

We show existence andWloc2,p ⋂ W1,∞-regularity results for the integro-differential equation, associated with a diffusion process with jumps on a bounded domain. The second order elliptic partial differential operator and the integral operator involved here are both maximum principle type operators, which enables us to makeW1,∞ a priori estimates.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bensoussan A (1978) On the Hamilton-Jacobi approach for the optimal control of diffusion processes with jumps. In: Friedman A, Pinsky M (eds) Stochastic analysis. Academic Press, New York, pp 25–55Google Scholar
  2. 2.
    Bensoussan A, Lions JL (to appear) Applications des inéquations variationelles en contrôle stochastique, vol. 2. Dunod, ParisGoogle Scholar
  3. 3.
    Bensoussan A, Menaldi JL (preprint) Optimal stochastic control of diffusion processes with jumps stopped at the exit of a domain.Google Scholar
  4. 4.
    Friedman A (1969) Partial differential equations. Holt, Rinehart, and Winston, New YorkGoogle Scholar
  5. 5.
    Gihman II, Skorohod AV (1979) The theory of stochastic processes III. Springer-Verlag, New YorkGoogle Scholar
  6. 6.
    Gilbarg D, Trudinger N (1977) Elliptic partial differential equations of second order. Springer-Verlag, New YorkGoogle Scholar
  7. 7.
    Lepeltier JP, Marchal B (1977) Sur l'existence de politiques optimales dans le contrôle integro-differential. Ann Inst Henri Poincare 12:45–97Google Scholar
  8. 8.
    Lions PL (1978) Resolution de problemes de Bellman-Dirichlet. C R Acad Sc Paris 287:747–750 (sèrie A). Also (detailed article to appear) Acta MathematicaGoogle Scholar
  9. 9.
    Stroock DW (1975) Diffusion processes associated with Levy generators. A Wahr Verw Gebiete 32:209–244Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Suzanne Lenhart
    • 1
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

Personalised recommendations