Randomized Euler-Maruyama achieves strong Lp order 1/2 + min(alpha, beta/2) - epsilon for additive SDEs with alpha-Holder time and beta-Holder space drift, improving on standard Euler-Maruyama.
The Milstein scheme for singular SDEs with H\"older continuous drift
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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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Randomised Euler-Maruyama method for SDEs with H\"older continuous drift coefficient
Randomized Euler-Maruyama achieves strong Lp order 1/2 + min(alpha, beta/2) - epsilon for additive SDEs with alpha-Holder time and beta-Holder space drift, improving on standard Euler-Maruyama.