This study finds that an Euler-Maruyama numerical scheme converges for SDEs with a drift in Besov space, suggesting effective implementation for complex drift functions.
This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function in the spatial variable, in particular being a 1/2-H\"older continuous function of time taking values in a H\"older-Zygmund space C-γ of negative order -γ<0. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong L¹ convergence rate. We finally implement the scheme and discuss the results obtained.
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Jáquez et al. (2025) studied this question.
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