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Journal of Theoretical Probability

, Volume 32, Issue 4, pp 1892–1908 | Cite as

Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

  • Olivier Menoukeu-Pamen
  • Youssef Ouknine
  • Ludovic TangpiEmail author
Article

Abstract

In this paper, we review and improve pathwise uniqueness results for some types of one-dimensional stochastic differential equations (SDE) involving the local time of the unknown process. The diffusion coefficient of the SDEs we consider is allowed to vanish on a set of positive measure and is not assumed to be smooth. As opposed to various existing results, our arguments are mainly based on the comparison theorem for local time and the occupation time formula. We apply our pathwise uniqueness results to derive strong existence and other properties of solutions for SDEs with rough coefficients.

Keywords

Stochastic differential equations Pathwise uniqueness Comparison theorem for local times Local time of the unknown 

Mathematics Subject Classification

60H10 60H60 60J55 

Notes

Acknowledgements

Financial support from the Alexander von Humboldt Foundation under the programme financed by the German Federal Ministry of Education and Research entitled German Research Chair No. 01DG15010 is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.African Institute for Mathematical SciencesBiriwaGhana
  2. 2.University of GhanaAccraGhana
  3. 3.Department of Mathematical SciencesInstitute for Financial and Actuarial MathematicsLiverpoolUK
  4. 4.Complex Systems Engineering and Human SystemsMohammed VI Polytechnic UniversityBen GuerirMorocco
  5. 5.Mathematics Department, FSSMCadi Ayyad UniversityMarrakeshMorocco
  6. 6.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

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