MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE

doi:10.1007/s10473-021-0312-0

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 827-842.doi: 10.1007/s10473-021-0312-0

MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE

孙晓霞¹, 郭峰²

1. School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

收稿日期:2019-11-05 修回日期:2020-06-08 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Xiaoxia SUN E-mail:xiaoxiasun@dufe.edu.cn
作者简介:Feng GUO,E-mail:fguo@dlut.edu.cn
基金资助:
The first author is supported by the National Natural Science Foundation of China (11801064).

MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE

Xiaoxia SUN¹, Feng GUO²

1. School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, China;
2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received:2019-11-05 Revised:2020-06-08 Online:2021-06-25 Published:2021-06-07
Contact: Xiaoxia SUN E-mail:xiaoxiasun@dufe.edu.cn
About author:Feng GUO,E-mail:fguo@dlut.edu.cn
Supported by:
The first author is supported by the National Natural Science Foundation of China (11801064).

摘要/Abstract

摘要： In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, which is obtained via its pull back formula and the Bismut method.

关键词: Fractional Ornstein-Uhlenbeck measure, integration by parts formula, martingale representation theorem, Logarithmic-Sobolev inequality

Abstract: In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, which is obtained via its pull back formula and the Bismut method.

Key words: Fractional Ornstein-Uhlenbeck measure, integration by parts formula, martingale representation theorem, Logarithmic-Sobolev inequality

中图分类号:

60G15

孙晓霞, 郭峰. MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE[J]. 数学物理学报(英文版), 2021, 41(3): 827-842.

Xiaoxia SUN, Feng GUO. MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE[J]. Acta mathematica scientia,Series B, 2021, 41(3): 827-842.

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MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE

MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE

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