Advances in Analysis

Download PDF (794.5 KB) PP. 125 - 142 Pub. Date: October 8, 2018

DOI: 10.22606/aan.2018.34001

• Eleonora Catsigeras^*
  Instituto de Matemática y Estadística "Rafael Laguardia", Universidad de la República, Uruguay

We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and pointwise ergodic theorems for the transfer operators associated to such systems. The results are extensions to noisy systems of some of the fundamental ergodic theorems for deterministic systems. The proofs are analytic. They follow the rigorous deductive method of the classic proofs in pure mathematics.

Ergodic theorems, transfer operator, stochastic systems, noisy dynamics.

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