An Introduction to Ergodic Theory
Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time average exists and is equal to the space average. The applications of ergodic theory are the main concern of this note. We will introduce fundamental concepts in ergodic theory, Birkhoff’s ergodic theorem and its consequences.
KeywordsBenford’s law Ergodic theorem Markov chain Measure-preserving transformation Poincaré’s recurrence theorem Strong-mixing Weak-mixing
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