In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy exponential distribution. Similar results are obtained for random expanding maps. We emphasize that what we establish is a quenched exponential law for hitting times. © 2014 Elsevier B.V. All rights reserved.
Rousseau, J., Saussol, B., & Varandas, P. (2014). Exponential law for random subshifts of finite type. Stochastic Processes and Their Applications, 124(10), 3260–3276. https://doi.org/10.1016/j.spa.2014.04.016