Strong convergence of the Euler-Maruyama approximation for SDEs with unbounded drift

In this work, we prove strong convergence on small time interval of order for arbitrarily small of the Euler-Maruyama approximation for additive Brownian motion with Hölder continuous drift satisfying a linear growth condition. The proof is based on direct estimations of functional of the Euler-Maru...

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Bibliographic Details
Published in:Stochastic analysis and applications 2023-05, Vol.41 (3), p.545-563
Main Authors: Babi, Akli O. L., Dieye, Moustapha, Pamen, Olivier Menoukeu
Format: Article
Language:English
Subjects:
Approximation
Brownian motion
Convergence
Drift
Euler-Maruyama approximation
Kolmogorov backward equation
Mathematical analysis
Primary 99Z99
Secondary 00A00
unbounded drifts
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Summary:In this work, we prove strong convergence on small time interval of order for arbitrarily small of the Euler-Maruyama approximation for additive Brownian motion with Hölder continuous drift satisfying a linear growth condition. The proof is based on direct estimations of functional of the Euler-Maruyama approximation. The order of convergence does not depend on the Hölder index of the drift, thus generalizing the results obtained in [10] to both Linear growth and to an optimal convergence order.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2022.2047726