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Strong rate of convergence for the Euler--Maruyama scheme of SDEs with unbounded Hölder continuous drift coefficient

In this paper, we provide the strong rate of convergence for the Euler--Maruyama scheme for multi-dimensional stochastic differential equations with uniformly locally (unbounded) Hölder continuous drift and multiplicative noise. Our technique is based on Itô--Tanaka trick (Zvonkin transformation) for unbounded drift. Moreover, in order to apply the stochastic sewing lemma, we use the heat kernel estimate for the density function of the Euler--Maruyama scheme.

preprint2026arXivOpen access
Tsukasa MoritokiDai Taguchi
math.PR
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Tsukasa MoritokiDai Taguchi

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