具有无界漂移的SDEs的Euler-Maruyama近似的强收敛性

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2022-03-23 DOI:10.1080/07362994.2022.2047726

Akli O. L. Babi, M. Dieye, O. M. Pamen

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引用次数: 0

摘要

摘要本文证明了具有Hölder连续漂移的加性布朗运动的Euler-Maruyama近似在满足线性增长条件的任意小阶时间区间上的强收敛性。证明是基于欧拉-丸山近似的泛函的直接估计。收敛阶不依赖于漂移的Hölder指数，从而将[10]中得到的结果推广到线性增长和最优收敛阶。

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

Abstract 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.

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来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.