Skip to main content
Log in

On solutions to stochastic differential equations with discontinuous drift in Hilbert space

  • 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.

References

  1. Berman, N., Root, W.L.: A weak stochastic integral in Banach space with application to a linear stochastic differential equation. Appl. Math. Optim.10, 97–125 (1983)

    Google Scholar 

  2. Bourbaki, N.: Topologie générale. Paris: Hermann 1974

    Google Scholar 

  3. Curtain, R.F.: Stochastic evolution equations with general white noise disturbance. J. Math. Anal. Appl.60, 570–595 (1977)

    Google Scholar 

  4. Curtain, R.F.: Linear stochastic Itô equations in Hilbert space. Lecture Notes in Control and Information Sciences, Vol. 16, pp. 61–84. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  5. Curtain, R.F.: Markov processes generated by linear stochastic evolution equations. Stochastics5, 135–165 (1981)

    Google Scholar 

  6. Curtain, R.F., Falb, P.L.: Stochastic differential equations in Hilbert spaces. J. Differential Equations10, 412–430 (1971)

    Google Scholar 

  7. Curtain, R.F., Pritchard, A.J.: Infinite dimensional linear systems theory. Lecture Notes in Control and Information Sciences, Vol. 8. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  8. Da Prato, D., Ianelli, M., Tubaro, L.: Semi-linear stochastic differential equations in Hilbert spaces. Boll. UMI16 A, 168–185 (1979)

    Google Scholar 

  9. Dieudonné, J.: Foundations of modern analysis. New York, London: Academic Press 1969

    Google Scholar 

  10. Doss, H., Royer, G.: Processus de diffusion associé aux mesures de Gibbs sur\(\mathbb{R}^{\mathbb{Z}^d } \). Z. Wahrscheinlichkeitstheorie u. verw. Gebiete46, 125–158 (1979)

    Google Scholar 

  11. Ibragimov, I.A., Rozanov, Y.A.: Gaussian random processes. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  12. Leha, G., Ritter, G.: On diffusion processes and their semi-groups in Hilbert spaces with an application to interacting stochastic systems. Ann. Probability (to appear)

  13. Métivier, M.: Semimartingales. Studies in Mathematics 2. Berlin, New York: de Gruyter 1982

    Google Scholar 

  14. Métivier, M., Pistone, G.: Sur une équation d'évolution stochastique. Bull. Soc. math. France104, 65–85 (1976)

    Google Scholar 

  15. Nelson, E.: Probability theory and Euclidean field theory. Lecture Notes in Physics, Vol. 25, pp. 94–124. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  16. Shiga, T., Shimizu, A.: Infinite dimensional differential equations and their applications. J. Math. Kyoto Univ.20, 395–416 (1980)

    Google Scholar 

  17. Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leha, G., Ritter, G. On solutions to stochastic differential equations with discontinuous drift in Hilbert space. Math. Ann. 270, 109–123 (1985). https://doi.org/10.1007/BF01455536

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01455536

Keywords

Navigation