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Pathwise uniqueness and approximation of solutions of stochastic differential equations

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Stochastic Differential Equation
  • Successive Approximation
  • Predictable Process
  • Unique Strong Solution
  • Uniform Integrability

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

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