Approximation of occupation time functionals

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-11-01 DOI:10.3150/21-BEJ1328

R. Altmeyer

引用次数: 9

Abstract

The strong L2-approximation of occupation time functionals is studied with respect to discrete observations of a d-dimensional cadlag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous results in the literature considerably. The approach relies on regularity for the marginals of the process and applies also to non-Markovian processes, such as fractional Brownian motion. The results are used to approximate occupation times and local times. For Brownian motion, the upper bounds are shown to be sharp up to a log-factor.

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占用时间泛函的逼近

针对d维时滞过程的离散观测，研究了占用时间泛函的强L2近似。在弱假设下获得了误差的上限，相当程度地推广了文献中先前的结果。该方法依赖于过程边缘的正则性，也适用于非马尔可夫过程，如分数布朗运动。结果用于近似占用时间和当地时间。对于布朗运动，上限被证明是尖锐的，直到对数因子。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.