Related papers: Stable CLT for deterministic systems

We consider the dynamical system described by the area--preserving standard mapping. It is known for this system that $P(t)$, the normalized number of recurrences staying in some given domain of the phase space at time $t$ (so-clled…

We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…

We consider a random field, defined on an integer-valued d-dimensional lattice, with covariance function satisfying a condition more general than summability. Such condition appeared in the well-known Newman's conjecture concerning the…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

For a class of locally (but not necessarily uniformly) Lipschitz continuous $d$-dimensional observables over a Gibbs-Markov system, we show that convergence of (suitably normalized and centered) ergodic sums to a non-Gaussian stable vector…

We establish characterization results for the ergodicity of stationary symmetric $\alpha$-stable (S$\alpha$S) and $\alpha$-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in…

For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set.…

The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…

Anfuso and Rosch [Phys. Rev. B 75, 144420 (2007)] showed that the "topological" Haldane phase in a fermionic spin-1/2 ladder can be continuously deformed into a "trivial" phase without explicitly breaking symmetries when local charge…

In this study, we consider the following extended attraction chemotaxis system of two species parabolic-parabolic-elliptic type with nonlocal terms \[ \begin{cases} u_t=d_1\Delta u-\chi_1\nabla (u\cdot \nabla…

In these notes, we obtain new stability estimates for centered non-degenerate selfdecomposable probability measures on $\mathbb{R}^d$ with finite second moment and for non-degenerate symmetric $\alpha$-stable probability measures on…

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying $SL_2$ symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can…

A symmetric pair of reductive groups $(G,H,\theta)$ is called stable, if every closed double coset of $H$ in $G$ is preserved by the anti-involution $g\mapsto \theta(g^{-1})$. In this paper, we develop a method to verify the stability of…

We study two dimensional freely decaying magnetohydrodynamic turbulence. We investigate the time evolution of the probability law of the gauge field and the stream function. Assuming that this probability law is initially defined by a…

Let $\mathcal X=\{\mathcal X_t:\, t\geq0,\, \mathcal X_0=0\}$ be a mean zero $\beta$-stable random walk on $\mathbb{Z}$ with inhomogeneous jump rates $\{\tau_i^{-1}: i\in\mathbb{Z}\}$, with $\beta\in(1,2]$ and $\{\tau_i: i\in\mathbb{Z}\}$ a…

In this paper we consider the existence of weakly c\`adl\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type…

We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient…

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…

We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…

Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M_1-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric…