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Pathwise uniqueness and approximation of solutions of stochastic differential equations

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Book cover Séminaire de Probabilités XXXII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1686))

Abstract

We consider stochastic differential equations for which pathwise uniqueness holds. By using Skorokhod's selection theorem we establish various strong stability results under perturbation of the initial conditions, coefficients and driving processes. Applications to the convergence of successive approximations and to stochastic control of diffusion processes are also given. Finally, we show that in the sense of Baire, almost all stochastic differential equations with continuous and bounded coefficients have unique strong solutions.

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Author information

Authors and Affiliations

  1. Dépt de maths, Université de Toulon et du Var B.P132, 83 957, La Garde Cedex, France

    Khaled Bahlali

  2. Institut d'hydraulique, Centre universitaire Med Khider, B.P. 145, Biskra, Algeria

    Brahim Mezerdi

  3. Dépt de maths, Fac. des sciences Semlalia, Université Cadi Ayyad Marrakech, Maroc

    Youssef Ouknine

Authors
  1. Khaled Bahlali
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  2. Brahim Mezerdi
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  3. Youssef Ouknine
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Jacques Azéma Marc Yor Michel Émery Michel Ledoux

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© 1998 Springer-Verlag

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Bahlali, K., Mezerdi, B., Ouknine, Y. (1998). Pathwise uniqueness and approximation of solutions of stochastic differential equations. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101757

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  • DOI: https://doi.org/10.1007/BFb0101757

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

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