Effective convergence in probability and an ergodic theorem for individual random sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 35-50
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An algorithmic analysis of the ergodic theorem for a measure-preserving transformation is given. We prove that the classical ergodic theorem is not algorithmically effective. We present a formulation and a proof of the ergodic theorem for individual random sequences based on A. N. Kolmogorov's algorithmic approach to the substantiation of the theory of probability and information theory.
Keywords:
ergodic theorem, quasiergodic theorem, stationary measure, convergence in probability, convergence almost everywhere, algorithm, random sequence, algorithmical randomness.
V. V. V'yugin. Effective convergence in probability and an ergodic theorem for individual random sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 35-50. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a2/
@article{TVP_1997_42_1_a2,
author = {V. V. V'yugin},
title = {Effective convergence in probability and an ergodic theorem for individual random sequences},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {35--50},
year = {1997},
volume = {42},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a2/}
}