Concentration of measure on product spaces with applications to Markov processes
Concentration of measure on product spaces with applications to Markov processes
复制标题
DOI：
10.4064/sm175-1-3
复制
发表时间：
2006
影响因子：
0.8
通讯作者：
G. Blower;F. Bolley
中科院分区：
文献类型：
--
作者：
G. Blower;F. Bolley
对于状态空间为某种Polish空间的随机过程，本文给出了联合律满足Gauss集中不等式和运输不等式的初始分布和条件分布的充分条件。在欧氏空间的情况下，存在联合律满足对数Sobolev不等式的充分条件。在几种情况下，所获得的常数相对于随机变量的数目是最优增长的，或者与这个数目无关。这些结果推广了Dobrushkin-Shlosman型条件下相互独立随机变量和弱相依随机变量的已知结果。本文还包含应用马尔可夫过程，包括阿尔马过程。
For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration and transportation inequalities. In the case of Euclidean space, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal growth with respect to the number of random variables, or are independent of this number. These results extend results known for mutually independent random variables and weakly dependent random variabels under Dobrushkin--Shlosman type conditions. The paper also contains applications to Markov processes including the ARMA process.