占用时间泛函的逼近

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2021-11-01 DOI:10.3150/21-BEJ1328

R. Altmeyer

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引用次数: 9

摘要

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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Approximation of occupation time functionals

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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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.