Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 827-842.doi: 10.1007/s10473-021-0312-0

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

Xiaoxia SUN1, Feng GUO2   

  1. 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).

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

CLC Number: 

  • 60G15
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