Dareiotis, K., Gerencsér, M., & Lê, K. (2023). Quantifying a convergence theorem of Gyöngy and Krylov. Annals of Applied Probability, 33(3), 2291–2323. https://doi.org/10.1214/22-AAP1867
E101-01 - Forschungsbereich Analysis E101 - Institut für Analysis und Scientific Computing
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Journal:
Annals of Applied Probability
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ISSN:
1050-5164
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Date (published):
Jun-2023
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Number of Pages:
33
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Publisher:
INST MATHEMATICAL STATISTICS-IMS
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Peer reviewed:
Yes
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Keywords:
Euler–Maruyama scheme; regularisation by noise; stochastic differential equations; rate of convergence; strong approximation
en
Abstract:
We derive sharp strong convergence rates for the Euler–Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order α ∈ (0, 1) lead to rate (1+α)/2.
