Geodesic
Probabilistic shadowing for pseudotrajectories with decreasing errors
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 207-229

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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. 
@article{ZNSL_2021_505_a12,
     author = {V. A. Priezzhev and P. A. Priezzhev and S. B. Tikhomirov},
     title = {Probabilistic shadowing for pseudotrajectories with decreasing errors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--229},
     publisher = {mathdoc},
     volume = {505},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a12/}
}
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V. A. Priezzhev; P. A. Priezzhev; S. B. Tikhomirov. Probabilistic shadowing for pseudotrajectories with decreasing errors. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 207-229. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a12/