Skip to main content
Log in

The martingale problem for a class of pseudo differential operators

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bass, R.F.: Uniquencess in law for pure jump Markov processes. Probab. Theory Relat. Fields79, 271–287 (1988)

    Google Scholar 

  2. Berg, C., Forst, G.: Potential theory on locally compact Abelian groups. (Ergeb. Math. Grenzgeb., II. Ser. Bd. 87) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  3. Courrège, P.: Sur la forme intégro-différentielle des opérateurs deC k dansC satisfaisant au principe du maximum. Sém. Théor. du Potentiel 38 p. (1965/66)

  4. Ethier, S.N., Kurtz, Th.G.: Markov processes — characterization and convergence. Wiley Series in Probability and Mathematical Statistics, New York Chicester: Wiley 1986

    Google Scholar 

  5. Hoh, W.: Das Martingalproblem für eine Klasse von Pseudodifferentialopertoren. Dissertation, Universität Erlangen-Nürnberg, 1992

  6. Hoh, W.: Some commutator estimates for pseudo differential operators with negative definite functions as symbols. Integral Equations Oper. Theor.17, 46–53 (1993)

    Google Scholar 

  7. Jacob, N.: Feller semigroups, Dirichlet forms and pseudodifferential operators. Forum Math.4, 433–446 (1992)

    Google Scholar 

  8. Jacob, N.: Further pseudo differential operators generating Feller semigroups and Dirichlet forms. Rev. Mat. Iberoam.9, 373–407 (1993)

    Google Scholar 

  9. Jacob, N.: A class of Feller semigroups generated by pseudo differential operators. Math. Z.215, 151–166 (1994)

    Google Scholar 

  10. Komatsu, T.: Markov processes associated with certain integral-differential operators. Osaka J. Markov10, 271–303 (1973)

    Google Scholar 

  11. Komatsu, T.: On the martingale problem for generators of stable processes with perturbations. Osaka J. Math.21, 113–132 (1984)

    Google Scholar 

  12. Komatsu, T.: Pseudo-differential operators and Markov processes. J. Math. Soc. Japan36, 387–418 (1984)

    Google Scholar 

  13. Lepeltier, J.-P., Marchal, B.: Problème des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel. Ann. Inst. Poincaré, Vol. XII, no. 1 43–103 (1976)

    Google Scholar 

  14. Mikulevičius, R., Pragarauskas, H: On the existence and uniqueness of solutions to the martingale problem. Preprint, Vilnius 1–62 (1990)

  15. Mikulevičius, R., Pragarauskas, H.: On the existence and uniqueness of solutions to the the martingale problem associated with Lipschitz continuous Lévy's generator. Preprint, Vilnius 1–11 (1990)

  16. Negoro, A., Tsuchiya, M.: Stochastic processes and semigroups associated with degenerate Lévy generating operators. Stochastics Stoch. Rep.26, 29–61 (1989)

    Google Scholar 

  17. Stroock, D.W.: Diffusion processes associated with Lévy generators. Z. Wahrscheinlichkeitstheorie Verw. Geb.32, 209–244 (1975)

    Google Scholar 

  18. Stroock, D.W., Varadhan, S.R.S: Multidimensional diffusion processes. (Grundl. math. Wiss. 233) Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  19. Tanabe, H.: Equations of evolution. Monographs and Studies in Mathematics, Vol. 6. London San Francisco Melbourne: Pitman 1979

    Google Scholar 

  20. Tsuchiya, M.: Lévy measure with generalized polar decomposition and the associated SDE with jumps. Stochastics Stoch. Rep.38, 95–117 (1992)

    Google Scholar 

  21. Yosida, K.: Functional analysis (Grundl. math. Wiss. 123). Berlin Heidelberg New York: Springer 1980

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoh, W. The martingale problem for a class of pseudo differential operators. Math. Ann. 300, 121–147 (1994). https://doi.org/10.1007/BF01450479

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450479

Mathematics Subject Classification (1991)

Navigation