Skip to main content
SpringerLink
Log in

Logarithmic Sobolev inequalities for two-sided birth-death processes

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for α is also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Diacoins P, Saloff-Coste L. Logarithmic Sobolev inequalities for Finite Markov Chains [J]. Ann Appl Prob, 1996, 6: 695–750.

    Article  Google Scholar 

  2. Stroock D. Logarithmic Sobolev Inequalities for Gibbs States [J]. Lecture Notes in Math, 1993, 1563: 194–228.

    Article  MathSciNet  Google Scholar 

  3. Chen M F, Wang F Y. Estimates of Logarithmic Sobolev Constant: An Improvement of Barky-Emery Criterion [J]. J Funct Anal, 1997, 144(2): 287–300.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen M F. Nash Inequalities for General Symmetric Forms [J]. Acta Math Sci, 1999, 15(3): 353–370.

    Article  MATH  Google Scholar 

  5. Chen M F. Logarithmic Sobolev Inequalities for Symmetric Forms [J]. Sci in China(A), 2000, 30(43): 601–608.

    Google Scholar 

  6. Wang F Y. Sobolev Type Inequalities for General Symmetic Forms [J]. Proc AMS, 2000, 128: 3675–3682.

    Article  MATH  Google Scholar 

  7. Bobkov S G, Götze F. Exponential Integrability and Transporation Cost Related Logarithmic Sobolev Inequalities [J]. J Funct Anal, 1999, 163: 1–28.

    Article  MATH  MathSciNet  Google Scholar 

  8. Miclo L. An Example of Application of Discrete Hardy’s Inequalities [J]. Markov Process Related Fields, 1999, 5: 319–330.

    MATH  MathSciNet  Google Scholar 

  9. Mao Yonghua. Logarithmic Sobolev Inequalities for Birth-Death Process and Diffusion Process on the Line [J]. Chinese J Appl Stat Prob, 2002, 18(1): 94–100.

    Google Scholar 

  10. Yang Xiangqun. The Construction Theory of Denumerable Markov Processes [M]. New York: Wiely Press, 1990.

    Google Scholar 

  11. Wang Zikun, Yang Xiangqun. Birth and Death Processes and Markov Chains [M]. Beijing: Science Press, 1980(Ch).

    Google Scholar 

  12. Chen M F. Variational Formulas of Poincaré-Type Inequalities for Birth-Death Processes [J]. Acta Math Sci, 2003, 19(4): 625–644.

    Article  MATH  Google Scholar 

  13. Kantorovich L V K, Akilov G p. Functional Analysis [M]. Oxford: Pergamom Press, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Qingshan Yang & Fuqing Gao

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Hong Liu

Authors
  1. Qingshan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuqing Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fuqing Gao.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10271091)

Biography: YANG Qingshan (1981–), male, Ph.D. candidate, research direction: large deviation principle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, Q., Liu, H. & Gao, F. Logarithmic Sobolev inequalities for two-sided birth-death processes. Wuhan Univ. J. Nat. Sci. 13, 133–136 (2008). https://doi.org/10.1007/s11859-008-0202-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-008-0202-5

Key words

CLC number

Search

Navigation