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. 
View via Publisher
impan.pl
2 Citations
Highly Influential Citations
1
Methods Citations
1

2 Citations

A functional stable limit theorem for Gibbs–Markov maps

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

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

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

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

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

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

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

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

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

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

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

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…