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Explicit Strong Solutions Of Multidimensional Stochastic Differential Equations

Author

Listed:
  • MICHAEL A. KOURITZIN

    (Department of Mathematical and Statistical Sciences, University of Alberta)

  • BRUNO REMILLARD

    (Service de l’enseignement des methodes quantitatives de gestion, HEC)

Abstract

Herein, we characterize strong solutions of multidimensional stochastic differential equations (formula) that can be represented locally as (formula) where W is an multidimensional Brownian motion and U, (symbole) are continuous functions. Assuming that (symbole) is continuously differentiable, we find that (symbole) must satisfy a commutation relation for such explicit solutions to exist and we identify all drift terms b as well as U and (symbole) that will allow X to be represented in this manner. Our method is based on the existence of a local change of coordinates in terms of a diffeomorphism between the solutions X and the strong solutions to a simpler Ito integral equation.

Suggested Citation

  • Michael A. Kouritzin & Bruno Remillard, 2000. "Explicit Strong Solutions Of Multidimensional Stochastic Differential Equations," RePAd Working Paper Series lrsp-TRS368, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0102005
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    File URL: http://www.repad.org/ca/on/lrsp/TRS368.pdf
    File Function: First version, 2002
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    More about this item

    Keywords

    Diffeomorphism; Ito processes; explicit solutions.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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