IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200194.html
   My bibliography  Save this paper

Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

Author

Listed:
  • Baker, Christopher T. H.
  • Buckwar, Evelyn

Abstract

Results are presented on the stability of solutions of stochastic delay differential equations with multiplicative noise and of convergent numerical solutions obtained by a a method of Euler-Maruyama type. An attempt is made to provide a fairly self-contained presentation. A basic concept of the stability of a solution of an evolutionary stochastic delay differential equation is concerned with the sensitivity of the solution to perturbations in the initial function. We recall the stability definitions considered herein and show that an inequality of Halanay type (derivable via comparison theory)j and deterministic results can be employed to derive stability conditions for solutions of suitable equations. In practice, dosed form solutions of stochastic delay differential equations are unlikely to he available. In the second part of the paper a stability theory for numerical solutions (solutions of Euler type) is considered. A convergence result is recalled for completeness and new stability results are obtained using a discrete analogue of the continuous Halanay-type inequality and results for a deterministic recurrence relation. Various results for stochastic (ordinary) differential equations with no time lag or for deterministic delay differential equations can he deduced from the results given here.

Suggested Citation

  • Baker, Christopher T. H. & Buckwar, Evelyn, 2001. "Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations," SFB 373 Discussion Papers 2001,94, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200194
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/62674/1/725962259.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Nehru, Vikram & Swanson, Eric & Dubey, Ashutosh, 1995. "A new database on human capital stock in developing and industrial countries: Sources, methodology, and results," Journal of Development Economics, Elsevier, vol. 46(2), pages 379-401, April.
    2. Fagerberg, Jan, 1994. "Technology and International Differences in Growth Rates," Journal of Economic Literature, American Economic Association, vol. 32(3), pages 1147-1175, September.
    3. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, pages 103-119.
    4. Benhabib, Jess & Spiegel, Mark M., 1994. "The role of human capital in economic development evidence from aggregate cross-country data," Journal of Monetary Economics, Elsevier, vol. 34(2), pages 143-173, October.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:200194. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/sfhubde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.