Large deviations principles for Markov chains and for strongly additive arithmetic functions
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Date
2015.
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Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015.
Abstract
Large deviations is a branch of probability theory with far-reaching applications in other elds of science and can be described to the layperson as the study of \very rare" events. We provide a modest introduction to the subject with an emphasis on large deviations behavior of continuous-time Markov chains and we present a recent result on large deviations related to the Erd}os-Kac theorem on the number of distinct prime factors of a uniformly chosen random natural number less than or equal to n.