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Ergodic Theorems and Related Problems (Hardcover, Reprint 2018)
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Ergodic Theorems and Related Problems (Hardcover, Reprint 2018)
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In the theory of random processes the term 'ergodicity' has a wide
variety of meanings. In the theory of stationary processes
ergodicity is often identified with metric transitivity. In the
theory of Markov processes, the word ergodic is applied to theorems
of both the existence of transition probability limits and on the
convergence of mean value ratios of these transition probabilities.
In addition, there are also 'ergodic theorems' on the convergence
of distributions of shifted random processes. In this monograph,
the term 'ergodic' is understood in its original sense, i.e. the
one it had when it was first adopted by the theory of random
processes from statistical mechanics and Boltzmann's theory of
gases. In this book, an ergodic theorem refers to any statement
about the existence of a mean value with respect to trajectories of
a random process taken with respect to time. The author takes the
view that problems of the existence of time means, and their
equality to phase means, are interesting without any assumptions
about the distribution of the random process.
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