منابع مشابه
A Marginal Ergodic Theorem
Michael Lavine Duke University, Durham, NC, USA. Summary. In recent years there have been several papers giving examples of Markov Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper (have infinite mass) and which therefore are not positive recurrent, yet which have subchains from which valid inference can be derived. These are nonergodic (not having a limiting distributio...
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This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
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Measure-preserving systems arise in a variety of contexts, such as probability theory, information theory, and of course in the study of dynamical systems. However, ergodic theory originated from statistical mechanics. In this setting, T represents the evolution of the system through time. Given a measurable function f : X → R, the series of values f(x), f(Tx), f(T x)... are the values of a phy...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1960
ISSN: 0019-2082
DOI: 10.1215/ijm/1255455860