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.

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.

@article{AMBP_2005__12_2_231_0,
     author = {Li, Guangfei and Miao, Yu and Peng, Huiming and Wu, Liming},
     title = {Poincar\'e and log-Sobolev inequality for stationary Gaussian processes and moving average processes},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {231--243},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {2},
     year = {2005},
     doi = {10.5802/ambp.205},
     zbl = {1090.60035},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2005__12_2_231_0/}
}
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/item/AMBP_2005__12_2_231_0/

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