arXiv subjects
Publications and source records attributed to Jonny Imbierski.
We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $α=1$-stable law. The focus of this work is on the method of proof via analytic techniques rather than the particular result.
In this article we derive a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets associated with non-autonomous dynamics constructed from families of countable affine iterated function systems. The formula obtained shows that the universal-lower-bound phenomenon present in the autonomous case studied by Fan et al. (2010) persists in this non-autonomous setting.
In this article, we calculate the Birkhoff spectrum in terms of the Hausdorff dimension of level sets for Birkhoff averages of continuous potentials for a certain family of diagonally affine IFS's. Also, we study Besicovitch-Eggleston sets for finite GLS number systems with redundancy. The redundancy refers to the fact that each number $x \in [0,1]$ has uncountably many expansions in the system. We determine the Hausdorff dimension of digit frequency sets for such expansions along fibres.
We obtain large deviations for a class of dependent random variables in the domain of attraction of an $α$-stable law, $α\in (0, 1)\cup (1, 2]$. This class includes ergodic sums of observables in the domain of attraction of an $α$-stable law driven by Gibbs-Markov maps.