# Functional limit theorem for occupation time processes of intermittent maps

@article{Sera2018FunctionalLT, title={Functional limit theorem for occupation time processes of intermittent maps}, author={Toru Sera}, journal={Nonlinearity}, year={2018}, volume={33}, pages={1183 - 1217} }

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 sense of strong distributional convergence. It is a functional and joint-distributional extension of Darling–Kac type limit theorem, of Lamperti type generalized arcsine laws for occupation times, and of Dynkin and Lamperti type generalized arcsine laws for waiting times, at the same time.

## 8 Citations

### Functional limits for"tied down"occupation time processes of infinite ergodic transformations

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. We prove functional, distributional limit theorems for the occupation times of pointwise dual ergodic transformations at “tied-down” times immediately after “excursions”. The limiting processes are…

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In their recent paper, Hata and Yano (2021 Stoch. Dyn. 2350006) first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points…

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In their recent paper [8], G. Hata and the fourth author first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points for which…

### Aging arcsine law in Brownian motion and its generalization.

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An aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution is derived.

### Doubly Intermittent Maps with Critical Points, Unbounded Derivatives and Regularly Varying Tail

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. We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing…

### Arcsine and Darling–Kac laws for piecewise linear random interval maps

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We give examples of piecewise linear random interval maps satisfying arcsine and Darling–Kac laws, which are analogous to Thaler’s arcsine and Aaronson’s Darling–Kac laws for the Boole…

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We compare ergodic properties of the kinetic energy for three stochastic models of subrecoil-laser-cooled gases. One model is based on a heterogeneous random walk (HRW), another is an HRW with…

### A functional stable limit theorem for Gibbs–Markov maps

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
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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…

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