Related papers: Central limit theorem and stable laws for intermit…

We establish a strong law of large numbers under intermediate trimming for a particular example of Birkhoff sums of a non-integrable observable over the doubling map. It has been shown in a previous work by Haynes that there is no strong…

We study Birkhoff sums as distributions. We obtain regularity results on such distributions for various dynamical systems with hyperbolicity, as hyperbolic linear maps on the torus and piecewise expanding maps on the interval. We also give…

We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the L\'evy…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

We investigate ergodic properties of a one-dimensional intermittent map that has not only an indifferent fixed point but also a singular structure such that a uniform measure is invariant under mapping. The most striking aspect of our model…

Let $f$ be a $C^{2+\epsilon}$ expanding map of the circle and $v$ be a $C^{1+\epsilon}$ real function of the circle. Consider the twisted cohomological equation $v(x) = \alpha (f(x)) - Df(x) \alpha (x)$ which has a unique bounded solution…

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…

We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity.

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…

We prove that infinitely renormalizable contracting Lorenz maps with bounded geometry or the so-called {\it a priori bounds} satisfies the slow recurrence condition to the singular point $c$ at its two critical values $c_1^-$ and $c_1^+$.…

We prove the Central Limit Theorem (CLT), the first order Edgeworth Expansion and a Mixing Local Central Limit Theorem (MLCLT) for Birkhoff sums of a class of unbounded heavily oscillating observables over a family of full-branch piecewise…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

We introduce a new framework that yields spectral bounds on norms of functions of transition maps for finite, homogeneous Markov chains. The techniques employed work for bounded semigroups, in particular for classical as well as for quantum…

We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$…

In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced $\rho'$-mixing condition.

We generalize Birkhoff's Theorem in the following fashion. We find necessary and sufficient conditions for any spherically symmetric space-time to be static in terms of the eigenvalues of the stress-energy tensor. In particular, we…

We study Birkhoff sums over rotations (series of the form $\sum_{r=1}^{N}\phi(r\alpha)$), in which the summed function $\phi$ may be unbounded at the origin. Estimates of these sums have been of significant interest and application in pure…

In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…