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 = {Guangfei Li and Yu Miao and Huiming Peng and Liming Wu}, 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 = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.205/} }
TY - JOUR AU - Guangfei Li AU - Yu Miao AU - Huiming Peng AU - Liming Wu TI - Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes JO - Annales mathématiques Blaise Pascal PY - 2005 SP - 231 EP - 243 VL - 12 IS - 2 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.205/ DO - 10.5802/ambp.205 LA - en ID - AMBP_2005__12_2_231_0 ER -
%0 Journal Article %A Guangfei Li %A Yu Miao %A Huiming Peng %A Liming Wu %T Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes %J Annales mathématiques Blaise Pascal %D 2005 %P 231-243 %V 12 %N 2 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.205/ %R 10.5802/ambp.205 %G en %F AMBP_2005__12_2_231_0
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, Volume 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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