Probabilistic shadowing for pseudotrajectories with decreasing errors

We consider the shadowing property of pseudotrajectories with decreasing errors for a linear skew product. The probabilistic properties of finite pseudotrajectories are studied. It is shown that for pseudotrajectories with errors decreasing exponentially, the typical dependence between the length of the pseudotrajectory and the shadowing accuracy is polynomial. The proof is based on the large deviation principle and the gambler's ruin problem.