Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Asymptotic properties of solutions of multidimensional stochastic differential equations
Download PDF
Download PDF
  • Published: June 1989

Asymptotic properties of solutions of multidimensional stochastic differential equations

  • G. Kersting1 

Probability Theory and Related Fields volume 82, pages 187–211 (1989)Cite this article

  • 76 Accesses

  • 1 Citations

  • Metrics details

Summary

LetX t ∈Rd be the solution of the stochastic equationdX t =b(X t )dt+δ(X t )dW t , whereW t denotes a standard Wiener process. The aim of the paper is to clarify under which conditions the drift term or the diffusion term is of negligible significance for the long term behaviour ofX t .

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Arnold, L., Oeljeklaus, E., Paradoux, E.: Almost sure and moment stability for linear Ito equations. Lect. Notes Math. vol. 1186, Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  2. Bhattacharya, R.N.: Criteria for recurrence and existence of invariant measures for multidimensional diffusions. Ann. Probab.6, 541–553 (1978)

    Google Scholar 

  3. Clark, C.R.: Asymptotic properties of some multidimensional diffusion. Ann. Probab.15, 985–1008 (1987)

    Google Scholar 

  4. Cranston, M.: Invariant δ-Fields for a class of diffusions. Z. Wahrscheinlichkeitstheor. Verw. Geb.65, 161–180 (1983)

    Google Scholar 

  5. Durrett, R.: Brownian motion and martingales in analysis. Belmont: Wadsworth 1984

    Google Scholar 

  6. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  7. Has'minskii, R.Z.: Stochastic stability of differential equations. Rockville: Alphen 1980

    Google Scholar 

  8. Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam: North Holland 1981

    Google Scholar 

  9. Keller, G., Kersting, G., Rösler, U.: On the asymptotic behaviour of solutions of stochastic differential equations. Z. Wahrscheinlichkeitstheor. Verw. Geb.68, 163–189 (1984)

    Google Scholar 

  10. Pinsky, R.: Recurrence, transience and bounded harmonic functions for diffusions in the plane. Ann. Probab.15, 954–984 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, J.W. Goethe-University, Postfach 11 19 32, D-6000, Frankfurt, Federal Republic of Germany

    G. Kersting

Authors
  1. G. Kersting
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kersting, G. Asymptotic properties of solutions of multidimensional stochastic differential equations. Probab. Th. Rel. Fields 82, 187–211 (1989). https://doi.org/10.1007/BF00354759

Download citation

  • Received: 14 June 1988

  • Revised: 03 March 1989

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00354759

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Differential Equation
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Stochastic Differential Equation
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature