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<div class="csl-entry">Gerencser, M. (2025, July 2). <i>The Milstein scheme revisited</i> [Presentation]. Workshop on Milstein’s method: 50 years on, Nottingham, United Kingdom of Great Britain and Northern Ireland (the). http://hdl.handle.net/20.500.12708/217633</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/217633
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dc.description.abstract
On its 50 year anniversary we revisit Milstein's second-order approximation scheme of stochastic differential equations that achieves strong convergence rate 1, as opposed to the 1/2 rate of the Euler-Maruyama scheme. Milstein's proof required four derivatives from drift and diffusion coefficients, which was later reduced to two by Wagner-Platen, relying on Ito-Taylor expansions. Here we provide a strict improvement by showing that strong convergence rate 1 holds assuming nothing else than the standard Lipschitz condition on the drift, if one sacrifices an arbitrarily small exponent in the rate. Additionally, we prove a central limit theorem that corrects a previously wrongly stated version in the literature.
