Ergodic Theorems for the Transfer Operators of Noisy Dynamical Systems
Ergodic Theorems for the Transfer Operators of Noisy Dynamical Systems is a scholarly work, published in 2018 in ''Advances in Analysis''. The main subjects of the publication include probabilistic logic, ergodic theory, Stationary ergodic process, distributed parameter system, pure mathematics, performance indicator, transfer, dynamical systems, mathematical proof, metric space, pointwise operation, chaos theory, discrete mathematics, transfer operator, dynamical systems theory, and mathematics. The authors 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.