Probabilistic shadowing in linear skew products

Abstract

We investigate the probability of shadowing of a random finite pseudotrajectory by an exact trajectory for linear skew products. We describe general conditions under which a random pseudotrajectory can be shadowed with polynomial (with respect to its length) precision with high probability. Examples satisfying that general condition are continuous linear skew products over Bernoulli shift, doubling map on a circle, and any Anosov linear map on a torus. The main tool used in the proof is Cramer's large deviation theorem.