非时齐马氏过程的Liggett-Stroock不等式

宋娟, 张铭

数学学报 ›› 2019, Vol. 62 ›› Issue (5) : 777-782.

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PDF(406 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (5) : 777-782. DOI: 10.12386/A2019sxxb0071
论文

非时齐马氏过程的Liggett-Stroock不等式

    宋娟1, 张铭2
作者信息 +

Liggett-Stroock Inequalities for Time Inhomogeneous Markov Processes

    Juan SONG1, Ming ZHANG2
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文章历史 +

摘要

本文将时齐马氏过程中重要的代数不等式Liggett-Stroock不等式推广到非时齐马氏过程中,建立了非时齐马氏过程的转移半群与Liggett-Stroock不等式之间的关系.

Abstract

We generalize the Liggett-Stroock 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 Liggett-Stroock inequality.

关键词

非时齐马氏过程 / 泛函不等式 / Liggett-Stroock不等式

Key words

inhomogeneous Markov processes / functional inequalities / Liggett-Stroock inequalities

引用本文

导出引用
宋娟, 张铭. 非时齐马氏过程的Liggett-Stroock不等式. 数学学报, 2019, 62(5): 777-782 https://doi.org/10.12386/A2019sxxb0071
Juan SONG, Ming ZHANG. Liggett-Stroock Inequalities for Time Inhomogeneous Markov Processes. Acta Mathematica Sinica, Chinese Series, 2019, 62(5): 777-782 https://doi.org/10.12386/A2019sxxb0071

参考文献

[1] Bakry D., Émery M., Hypercontractivité de semi-groupes de diffusion, C. R. Acad. Sci. Paris Sér, I Math., 1984, 299:775-778.
[2] Chen M. F., From Markov Chains to Non-equilibrium Particle Systems, Second Edition, World Scientific, Beijing, 2004.
[3] Chen M. F., Wang Y. Z., Algebraic convergence of Markov chains, Annals of Applied Probability, 2003, 13(2):604-627.
[4] Liggett T. M., L2 rates of convergence for attractiver reversible nearest particle systems:The critical case, Ann. Probab., 1991, 19:935-959.
[5] Röckner M., Wang F. Y., Weak Poincaré inequalities and L2-convergence rates of Markov semigroups, Journal of Functional Analysis, 2001, 185(2):564-603.
[6] Zhang M., Nash inequalities for time inhomogeneous Markov processes (in Chinese), Scientia Sinica Math., 2018, 48(8):1053-1060.

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