Strong convergence of the Euler-Maruyama approximation for SDEs with unbounded drift. Issue 3 (4th May 2023)

• Record Type: Journal Article
• Authors: Babi, Akli O. L.; Dieye, Moustapha; Pamen, Olivier Menoukeu
• Is Part Of: Stochastic analysis and applications. Volume 41:Issue 3(2023)
• Page Start: 545
• Page End: 563
• Publication Date: 2023-05-04
• Subjects: Euler–Maruyama approximation -- unbounded drifts -- Kolmogorov backward equation; Primary 99Z99 -- Secondary 00A00; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2022.2047726
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this work, we prove strong convergence on small time interval of order 1 / 2 − ϵ for arbitrarily small ϵ > 0 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.