Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
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
Annales mathématiques Blaise Pascal (2005)
- Volume: 12, Issue: 2, page 231-243
- ISSN: 1259-1734
Access Full Article
top
Abstract
topHow to cite
topLi, Guangfei, et al. "Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes." Annales mathématiques Blaise Pascal 12.2 (2005): 231-243. <http://eudml.org/doc/10518>.
@article{Li2005,
abstract = {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.},
affiliation = {Wuhan University Dep. of Mathematics Hubei, MA 430072 CHINA; Wuhan University Dep. of Mathematics Hubei, MA 430072 CHINA; Wuhan University Dep. of Mathematics Hubei, MA 430072 CHINA; Université Blaise Pascal Lab. de Mathématiques CNRS-UMR 6620 63177 Aubière France},
author = {Li, Guangfei, Miao, Yu, Peng, Huiming, Wu, Liming},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Poincaré inequality; logarithmic Sobolev inequality},
language = {eng},
month = {7},
number = {2},
pages = {231-243},
publisher = {Annales mathématiques Blaise Pascal},
title = {Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes},
url = {http://eudml.org/doc/10518},
volume = {12},
year = {2005},
}
TY - JOUR
AU - Li, Guangfei
AU - Miao, Yu
AU - Peng, Huiming
AU - Wu, Liming
TI - Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
JO - Annales mathématiques Blaise Pascal
DA - 2005/7//
PB - Annales mathématiques Blaise Pascal
VL - 12
IS - 2
SP - 231
EP - 243
AB - 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.
LA - eng
KW - Poincaré inequality; logarithmic Sobolev inequality
UR - http://eudml.org/doc/10518
ER -
References
top- F. Avram, On bilinear forms in Gaussian random variables and Toeplitz matrices, Probab. Th. Rel. Fields 79 (1988), 37-45 Zbl0648.60043MR952991
- H. Djellout, A. Guillin, L. Wu, Moderate deviations of moving average processes Zbl1100.60010
- M.D. Donsker, S.R.S. Varadhan, Large deviations for stationary Gaussian processes, Comm. Math. Phys. 97 (1985), 187-210 Zbl0646.60030MR782966
- M. Gourcy, L. Wu, Log-Sobolev inequalities for diffusions with respect to the -metric Zbl1098.60027
- M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilités XXXIII. Lecture Notes in Mathematics 1709 (1999), 120-216 Zbl0957.60016MR1767995
- L Grossn, Logarithmic Sobolev inequalities and contractivity properties of semigroups, Varenna, 1992, Lecture Notes in Math. 1563 (1993), 54-88 Zbl0812.47037MR1292277
- S.G Bobkov, F Gotze, Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities, J. Funct. Anal. 163, No.1 (1999), 1-28 Zbl0924.46027MR1682772
- M.S. Taqqu, Fractional Brownian motion and long-range dependence, Theory and applications of long-range dependence (2003), 5-38 Zbl1039.60041MR1956042
- L. Wu, On large deviations for moving average processese, Probability, Finance and Insurance, pp.15-49, the proceeding of a Workshop at the University of Hong-Kong (15-17 July) (2002) MR2189197
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.