The compound Poisson distribution and return times in dynamical systems
By N. Haydn, Sandro Vaienti. 2008
69 citations recorded by the source corpus.
Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/58cbd3dfa64998903c33fbb39a7543a37430a646
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Extreme value theory for non-uniformly expanding dynamical systems (2012, background): “There is also a closely related literature on return time statistics [3, 16, 14, 15, 17, 21].”