%A 孙晓霞, 郭峰 %T MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE %0 Journal Article %D 2021 %J 数学物理学报(英文版) %R 10.1007/s10473-021-0312-0 %P 827-842 %V 41 %N 3 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16399.shtml} %8 2021-06-25 %X 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.