A coupling approach to random circle maps expanding on the average

作者：Stenlund Mikko^*; Sulku Henri

来源：Stochastics and Dynamics, 2014, 14(4): 1450008.

DOI：10.1142/S0219493714500087

• Random maps expanding on the average
• coupling
• memory loss
• correlation decay
• almost sure invariance principle

We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential mixing. Leveraging from the structure of the associated correlation estimates, we prove an almost sure invariance principle for vector-valued observables. The motivation for our paper is to explore these methods in a non-uniform random setting.

• 出版日期2014-12