Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
Li, Guangfei1 ; Miao, Yu1 ; Peng, Huiming1 ; Wu, Liming2
1 Wuhan University Dep. of Mathematics Hubei, MA 430072 CHINA
2 Université Blaise Pascal Lab. de Mathématiques CNRS-UMR 6620 63177 Aubière France
Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 2, pp. 231-243.

For stationary Gaussian processes, we obtain the necessary and sufficient conditions for Poincaré inequality and log-Sobolev inequality of process-level and provide the sharp constants. The extension to moving average processes is also presented, as well as several concrete examples.

DOI : 10.5802/ambp.205
Li, Guangfei 1 ; Miao, Yu 1 ; Peng, Huiming 1 ; Wu, Liming 2

1 Wuhan University Dep. of Mathematics Hubei, MA 430072 CHINA
2 Université Blaise Pascal Lab. de Mathématiques CNRS-UMR 6620 63177 Aubière France 
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Li, Guangfei; Miao, Yu; Peng, Huiming; Wu, Liming. Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes. Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 2, pp. 231-243. doi : 10.5802/ambp.205. http://www.numdam.org/articles/10.5802/ambp.205/

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