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A tamed Euler scheme for SDEs with non-locally integrable drift coefficient

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  • Johnston, Tim
  • Sabanis, Sotirios

Abstract

In this article we show that for SDEs with a drift coefficient that is non-locally integrable, one may define a tamed Euler scheme that converges in Lp at rate 1/2 to the true solution. The taming is required in this case since one cannot expect the regular Euler scheme to have finite moments in Lp. Our proof strategy involves controlling the inverse moments of the distance of scheme and the true solution to the singularity set. We additionally show that our setting applies to the case of two scalar valued particles with singular interaction kernel. To the best of the authors’ knowledge, this is the first work to prove strong convergence of an Euler-type scheme in the case of non-locally integrable drift.

Suggested Citation

  • Johnston, Tim & Sabanis, Sotirios, 2026. "A tamed Euler scheme for SDEs with non-locally integrable drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002169
    DOI: 10.1016/j.spa.2025.104772
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    References listed on IDEAS

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    1. Dalalyan, Arnak S. & Karagulyan, Avetik, 2019. "User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5278-5311.
    2. Zhang, Xicheng, 2005. "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1805-1818, November.
    3. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
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