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

Abstract

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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.

How to cite

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Li, 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

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  1. F. Avram, On bilinear forms in Gaussian random variables and Toeplitz matrices, Probab. Th. Rel. Fields 79 (1988), 37-45 Zbl0648.60043MR952991
  2. H. Djellout, A. Guillin, L. Wu, Moderate deviations of moving average processes Zbl1100.60010
  3. M.D. Donsker, S.R.S. Varadhan, Large deviations for stationary Gaussian processes, Comm. Math. Phys. 97 (1985), 187-210 Zbl0646.60030MR782966
  4. M. Gourcy, L. Wu, Log-Sobolev inequalities for diffusions with respect to the L 2 -metric Zbl1098.60027
  5. M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Séminaire de Probabilités XXXIII. Lecture Notes in Mathematics 1709 (1999), 120-216 Zbl0957.60016MR1767995
  6. L Grossn, Logarithmic Sobolev inequalities and contractivity properties of semigroups, Varenna, 1992, Lecture Notes in Math. 1563 (1993), 54-88 Zbl0812.47037MR1292277
  7. 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
  8. M.S. Taqqu, Fractional Brownian motion and long-range dependence, Theory and applications of long-range dependence (2003), 5-38 Zbl1039.60041MR1956042
  9. 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

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