分式奥恩斯坦-乌伦贝克过程中参数估计的适度偏差与 $$H \ in (0,{1\over 2})$$

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI:10.1007/s10255-024-1083-x

Hui Jiang, Qing-shan Yang

{"title":"分式奥恩斯坦-乌伦贝克过程中参数估计的适度偏差与 $$H \\ in (0,{1\\over 2})$$","authors":"Hui Jiang, Qing-shan Yang","doi":"10.1007/s10255-024-1083-x","DOIUrl":null,"url":null,"abstract":"In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index \$H \\in (0,{1 \\over 2})\$. The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"34 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with $$H \\\\in (0,{1 \\\\over 2})$$\",\"authors\":\"Hui Jiang, Qing-shan Yang\",\"doi\":\"10.1007/s10255-024-1083-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index \\\$H \\\\in (0,{1 \\\\over 2})\\\$. The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10255-024-1083-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10255-024-1083-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有赫斯特指数（H \in (0,{1 \over 2})\）的遍历分数奥恩斯坦-乌伦贝克过程中漂移函数中两个参数的估计值的渐近性质。可以得到克拉梅尔型温和偏差以及具有明确速率函数的温和偏差。主要方法包括多重维纳-伊托积分的偏差不等式和克拉梅尔型温和偏差，以及渐近分析技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with $$H \in (0,{1 \over 2})$$

In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index $H \in (0,{1 \over 2})$. The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.