Hellinger和近似Lévy驱动SDE的总变差距离

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-03-17 DOI:10.1214/22-aap1863

E. Cl'ement

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引用次数: 2

摘要

本文在L{\'e}vy驱动的随机微分方程的驱动过程是局部稳定的情况下，得到了其离散路径的近似在总变差距离上的收敛速率。研究了欧拉近似的特殊情况。我们的结果是基于使用Malliavin微积分对跳跃过程获得的海灵格距离的尖锐局部估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hellinger and total variation distance in approximating Lévy driven SDEs

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of L{\'e}vy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.