Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space

09/20/2023

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by   Luis Mario Chaparro Jáquez, et al.

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This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Holder-Zygmund space C^-γ of negative order -γ<0 in the spacial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong L^1 convergence rate. We finally implement the scheme and discuss the results obtained.