
离散时间Markov链几何非常返与代数非常返的判别准则
Criteria for Geometric and Algebraic Transience for Discrete-time Markov Chains
本文研究可数状态空间离散时间Markov链的几何非常返和代数非常返,利用某状态末离时的矩条件和某方程解的存在性,给出两种非常返性的判别准则.进一步,我们将所得结果应用于研究Geom/G/1排队模型的随机稳定性.
We study geometric and algebraic transience for discrete-time Markov chains on countable state spaces. Criteria are presented based on the moment of the last exit time for some state and the existence of solution for some equation. Moreover, we apply the results to investigating the stochastic stability of Geom/G/1 queueing models.
几何非常返 / 代数非常返 / 末离时 / 最小非负解 / Geom/G/1排队模型 {{custom_keyword}} /
geometric transience / algebraic transience / last exit time / the minimal non-negative solution / Geom/G/1 queueing model {{custom_keyword}} /
[1] Anderson W., Continuous-Time Markov Chains, Springer-Verlag, New York, 1991.
[2] Asmussen S., Applied Probability and Queues, 2nd ed., Springer-Verlag, New York, 2003.
[3] Aurzada F., Iksanov A., Meiners M., Exponential moments of first passage times and related quantities for Lévy processes, Math. Nachr., 2015, 288(17-18):1921-1938.
[4] Chen M. F., From Markov Chains to Non-equilibrium Particle Systems, 2nd ed., World Scientific, Singapore, 2004.
[5] Chen M. F., Eigenvalues, Inequalities and Ergodic Theory, Springer-Verlag, New York, 2005.
[6] Chen M. F., Speed of stability for birth-death processes, Front. Math. China, 2010, 5(3):379-515.
[7] Chen M. F., Basic estimates of stability rate for one-dimensional diffusions, Chapter 6 in "Probability Approximations and Beyond", Lecture Notes in Statistics, 2012, 205:75-99.
[8] Getoor R. K., Transience and recurrence of Markov processes, Séminaire de Probabilités (Strasbourg), 1980, 14:397-409.
[9] Hou Z. T., Guo Q. F., Homogeneous Denumerable Markov Processes, Springer-Verlag, New York, 1988.
[10] Iksanov A., Meiners M., Exponential moments of first passage times and related quantities for random walks, Electron. Commun. Probab., 2010, 15(34):365-375.
[11] Karlin S., Taylor H. M., A First Course in Stochastic Processes, 2nd ed., Academic Press, New York, 1975.
[12] Li J. P., Chen A. Y., Decay property of stopped Markovian bulk-arriving queues, Adv. Appl. Prob., 2008, 40(1):95-121.
[13] Mao Y. H., Algebraic convergence for discrete-time ergodic Markov chains, Sci. China Ser. A, 2003, 46(5):621-630.
[14] Mao Y. H., Song Y. H., Spectral gap and convergence rate for discrete-time Markov chains, Acta Math. Sinica, Engl. Ser., 2013, 29(10):1949-1962.
[15] Mao Y. H., Song Y. H., On geometric and algebraic transience for discrete-time Markov chains, Stoch. Proc. Appl., 2014, 124(4):1648-1678.
[16] Meyn S. P., Tweedie R. L., Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993.
国家自然科学基金资助项目(11501576);中南财经政法大学研究生教育创新计划项目(201821301)
/
〈 |
|
〉 |