A joint limit theorem for compactly regenerative ergodic transformations
@article{Kocheim2011AJL, title={A joint limit theorem for compactly regenerative ergodic transformations}, author={David Kocheim and Roland Zweim{\"u}ller}, journal={Studia Mathematica}, year={2011}, volume={203}, pages={33-45} }
We study conservative ergodic innite measure preserving transformations satisfying a compact regeneration property introduced in (Z4). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zn;Sn), where Zn and Sn respectively are the time of the last visit before time n to, and the occupation time of, a suitable set Y of nite measure.
2 Citations
A functional stable limit theorem for Gibbs–Markov maps
- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2023
We prove a weak invariance principle in the Skorohod $\mathcal{J}_{1}% $-topology for ergodic sums of locally (but not necessarily uniformly) Lipschitz continuous observables in the domain of…
Functional limit theorem for occupation time processes of intermittent maps
- MathematicsNonlinearity
- 2020
We establish a functional limit theorem for the joint-law of occupations near and away from indifferent fixed points of interval maps, and of waits for the occupations away from these points, in the…
References
SHOWING 1-10 OF 24 REFERENCES
Infinite measure preserving transformations with compact first regeneration
- Mathematics
- 2007
We study ergodic infinite measure preserving transformations T possessing reference sets of finite measure for which the set of densities of the conditional distributions given a first return (or…
Mixing Limit Theorems for Ergodic Transformations
- Mathematics
- 2007
Abstract
We show that distributional and weak functional limit theorems for ergodic processes often hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in…
Distributional limit theorems in infinite ergodic theory
- Mathematics
- 2006
We present a unified approach to the Darling-Kac theorem and the arcsine laws for occupation times and waiting times for ergodic transformations preserving an infinite measure. Our method is based on…
Measure preserving transformations similar to Markov shifts
- Mathematics
- 2009
Similarity, that is, the existence of joint common extensions, defines an interesting equivalence relation for infinite measure preserving transformations T. We provide a sufficient condition, given…
Ergodic properties of infinite measure-preserving interval maps with indifferent fixed points
- MathematicsErgodic Theory and Dynamical Systems
- 2000
We consider piecewise twice differentiable maps $T$ on $[0,1]$ with indifferent fixed points giving rise to infinite invariant measures, and we study their behaviour on ergodic components. As we do…
An introduction to infinite ergodic theory
- Mathematics
- 1997
Non-singular transformations General ergodic and spectral theorems Transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions…
Transformations on [0, 1] with infinite invariant measures
- Mathematics
- 1983
Under certain regularity conditions a real transformation with indifferent fixed points has an infinite invariant measure equivalent to Lebesgue measure. In this paper several ergodic properties of…
S-unimodal Misiurewicz maps with flat critical points
- Mathematics
- 2004
We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points.…
Hopf's ratio ergodic theorem by inducing
- Mathematics
- 2004
We present a very quick and easy proof of the classical StepanovHopf ratio ergodic theorem, deriving it from Birkho¤s ergodic theorem by a simple inducing argument. During the last few years, there…
ON OCCUPATION TIMES FOR MARKOFF PROCESSES
- Mathematics
- 1957
where u(t) is a suitable normalization. If V(x) is the characteristic function of a set, ftaV(x(r))dT is the occupation time of the set. The principal result is that under suitable (but quite…