Log-Sobolev Inequalities for Time Inhomogeneous Markov Processes

Juan SONG, Ming ZHANG

Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (4) : 747-752.

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PDF(373 KB)
Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (4) : 747-752. DOI: 10.12386/A20220009

Log-Sobolev Inequalities for Time Inhomogeneous Markov Processes

  • Juan SONG1, Ming ZHANG2
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Abstract

We generalize the classical log-Sobolev inequality of the time homogeneous Markov process to the inhomogeneous Markov process, and establish the relationship between the transition semigroup of inhomogeneous Markov process and the log-Sobolev inequality.

Key words

inhomogeneous Markov processes / functional inequality / log-Sobolev inequality

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Juan SONG, Ming ZHANG. Log-Sobolev Inequalities for Time Inhomogeneous Markov Processes. Acta Mathematica Sinica, Chinese Series, 2023, 66(4): 747-752 https://doi.org/10.12386/A20220009

References

[1] Bakry D., Emery M., Hypercontractivite de semi-groupes de diffusion, C. R. Acad. Sci., Paris Ser., I Math., 1984, 299: 775-778.
[2] Chen M. F., Nash inequalities for general symmetric forms, Acta Mathematica Sinica, English Series, 1999, 15(3): 353-370.
[3] Chen M. F., Wang Y. Z., Algebraic convergence of Markov chains, Annals of Applied Probability, 2003, 13(2): 604-627.
[4] Chen M. F., From Markov Chains to Non-equilibrium Particle Systems, World Scientufic, Second Edition, Beijing, 2004.
[5] Liggett T. M., L2 rates of convergence for attractiver reversible nearest particle systems: The critical case, Ann Probab, 1991, 19: 935-959.
[6] Song J., Zhang M., Liggett-Stroock inequalities for time inhomogeneous Markov processes (in Chinese), Acta Mathematica Sinica, 2019, 62(5): 777-782.
[7] Wang F. Y., Functional Inequalities, Markov Semigroups and Spectral Theory, Science Press, Beijing, 2006.
[8] Zhang M., Nash inequalities for time inhomogeneous Markov processes (in Chinese), Scientia Sinica Mathematica, 2018, 48(8): 1053-1060.
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