# 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

### 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…

### 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…

## References

SHOWING 1-10 OF 22 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…

### A limit theorem for sojourns near indifferent fixed points of one-dimensional maps

- MathematicsErgodic Theory and Dynamical Systems
- 2002

For a class of one-dimensional maps with two indifferent fixed points of the same order, a parallel to the arc-sine law for the number of positive partial sums of a real random walk is proved.

### The Dynkin-Lamperti arc-sine laws for measure preserving transformations

- Mathematics
- 1998

Arc-sine laws in the sense of renewal theory are proved for return time processes generated by transformations with infinite invariant measure on sets satisfying a type of Darling-Kac condition, and…

### Some Theorems on Functionals of Markov Chains

- Mathematics
- 1964

1. Introduction. In this paper we shall investigate various phenomena associated with a Markov process in discrete time, extending results found in [3], [6], [7], and [13]. The paper is divided into…