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Stochastic differential equations with singular drift

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  • Rutkowski, Marek

Abstract

We study the pathwise uniqueness of solutions of one-dimensional stochastic differential equations involving local times, under the assumption that the diffusion coefficient satisfies the (LT) condition introduced by Barlow and Perkins (1984). We show that this condition is sufficient for the pathwise uniqueness in the case of SDE's involving local times studied until now. In the final section a more general class of equations is introduced.

Suggested Citation

  • Rutkowski, Marek, 1990. "Stochastic differential equations with singular drift," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 225-229, August.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:3:p:225-229
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    Cited by:

    1. 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.
    2. Bachmann, Stefan, 2020. "On the strong Feller property for stochastic delay differential equations with singular drift," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4563-4592.

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