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Martingale Representation and Logarithmic-Sobolev Inequality for the Fractional Ornstein-Uhlenbeck Measure

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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.

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Authors and Affiliations

  1. School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian, 116025, China

    Xiaoxia Sun  (孙晓霞)

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Feng Guo  (郭峰)

Authors
  1. Xiaoxia Sun  (孙晓霞)
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  2. Feng Guo  (郭峰)
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Corresponding author

Correspondence to Xiaoxia Sun  (孙晓霞).

Additional information

The first author is supported by the National Natural Science Foundation of China (11801064).

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Sun, X., Guo, F. Martingale Representation and Logarithmic-Sobolev Inequality for the Fractional Ornstein-Uhlenbeck Measure. Acta Math Sci 41, 827–842 (2021). https://doi.org/10.1007/s10473-021-0312-0

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  • DOI: https://doi.org/10.1007/s10473-021-0312-0

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