Annales Mathématiques
Blaise Pascal
no. 2
Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
Guangfei Li1 ; Yu Miao1 ; Huiming Peng1 ; Liming Wu2
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

Guangfei Li 1 ; Yu Miao 1 ; Huiming Peng 1 ; Liming Wu 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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Guangfei Li; Yu Miao; Huiming Peng; Liming Wu. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.205/

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