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Genericity in Deterministic and Stochastic Differential Equations

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1755)

Abstract

We prove that the convergence of the approximation with time delay, as well as pathwise uniqueness, are generic properties in ordinary differential equations as well as in stochastic differential equations. This is done in the case where the coefficients are neither bounded nor time continuous. The approximation with time delay is used to obtain existence of weak solutions for SDE. We also prove L2-convergence of this approximation when only pathwise uniqueness is assumed.

Mathematics Subject Classification (2000):

  • 60GXX
  • 60HXX
  • 60JXX

Keywords:

  • Approximation with time delay
  • generic property
  • pathwise uniqueness
  • strong and weak solution

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Correspondence to J. J. Alibert .

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© 2001 Springer-Verlag Berlin/Heidelberg

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Alibert, J.J., Bahlali, K. (2001). Genericity in Deterministic and Stochastic Differential Equations. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXV. Lecture Notes in Mathematics, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44671-2_17

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  • DOI: https://doi.org/10.1007/978-3-540-44671-2_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41659-3

  • Online ISBN: 978-3-540-44671-2

  • eBook Packages: Springer Book Archive