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arXiv · 2305.16004

The Milstein scheme for singular SDEs with H\"older continuous drift

Máté Gerencsér·Gerald Lampl·Chengcheng Ling
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Abstract

We study the $L^p$ rate of convergence of the Milstein scheme for SDEs when the drift coefficients possess only H\"older regularity. If the diffusion is elliptic and sufficiently regular, we obtain rates consistent with the additive case. The proof relies on regularisation by noise techniques, particularly stochastic sewing, which in turn requires (at least asymptotically) sharp estimates on the law of the Milstein scheme, which may be of independent interest.

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Máté Gerencsér, Gerald Lampl, Chengcheng Ling. 2023-05-25. The Milstein scheme for singular SDEs with H\"older continuous drift. https://arxiv.org/abs/2305.16004

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