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Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients

Author

Listed:
  • Olivier Menoukeu-Pamen

    (African Institute for Mathematical Sciences
    University of Ghana
    Institute for Financial and Actuarial Mathematics)

  • Youssef Ouknine

    (Mohammed VI Polytechnic University
    Cadi Ayyad University)

  • Ludovic Tangpi

    (Princeton University)

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.

Suggested Citation

  • Olivier Menoukeu-Pamen & Youssef Ouknine & Ludovic Tangpi, 2019. "Pathwise Uniqueness of Non-uniformly Elliptic SDEs with Rough Coefficients," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1892-1908, December.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0869-2
    DOI: 10.1007/s10959-018-0869-2
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    References listed on IDEAS

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    1. Rutkowski, Marek, 1990. "Stochastic differential equations with singular drift," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 225-229, August.
    2. Étoré, Pierre & Martinez, Miguel, 2018. "Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2642-2687.
    Full references (including those not matched with items on IDEAS)

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