Related papers: Tail Invariant Measures of the Dyck Shift

A classical fact in ergodic theory is that ergodicity is equivalent to almost everywhere divergence of ergodic sums of all nonnegative integrable functions which are not identically zero. We show two methods, one in the measure preserving…

Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…

We prove that for every ergodic invariant measure with positive entropy of a continuous map on a compact metric space there is $\delta>0$ such that the dynamical $\delta$-balls have measure zero. We use this property to prove, for instance,…

Let $Y=\sum_{k\ge 1} 1_{A_k}$ be an infinite sum of the indicators of independent events. We investigate a precise (as opposed to logarithmic) first-order asymptotic behavior of the tail probabilities $\mathbb{P}\{Y\ge n\}$ and the point…

Given a factor code $\pi$ from a one-dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$, if $\pi$ is finite-to-one there is an invariant called the degree of $\pi$ which is defined the number of preimages of a typical…

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…

The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…

In this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…

We prove the finiteness of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms where the center direction has a dominated decomposition into one dimensional bundle and there is a uniform lower bound for the absolute…

We study finite measures on Bratteli diagrams invariant with respect to the tail equivalence relation. Amongst the proved results on finiteness of measure extension, we characterize the vertices of a Bratteli diagram that support an ergodic…

We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and…

Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper,…

It is well known that ergodic invariant measures for order preserving two-sided time random dynamical systems(RDS) on the real line $\mathbb R$ are Dirac. In the present note this is shown to hold also for one-sided time RDS.

Let $\pi:X\to Y$ be a factor map, where $(X,\sigma_X)$ and $(Y,\sigma_Y)$ are subshifts over finite alphabets. Assume that $X$ satisfies weak specification. Let $\ba=(a_1,a_2)\in \R^2$ with $a_1>0$ and $a_2\geq 0$. Let $f$ be a continuous…

For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We…

We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…

In this paper, we consider certain $\sigma$-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have…

We prove that, for a $C^2$ partially hyperbolic endomorphism of the 2-torus which is strongly transitive, given an ergodic $u$-Gibbs measure that has positive center Lyapunov exponent and has full support, then either the map is special…

This paper investigates the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of iterated homeomorphisms. It is shown that for the full two-shift, the collection of such invariant sets with the weak…

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…