Related papers: Strong invariance principles for dependent random …
In this paper, we investigate the law of large numbers for strictly stationary random fields, that is, we provide sufficient conditions on the moments and the dependence of the random field in order to guarantee the almost sure convergence…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…
In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev…
We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…
In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…
We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent non-identically distributed random variables. These results generalize Etemadi's extension of…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays $\{X_{n,k}, \, 1 \leqslant k \leqslant n, \, n \geqslant…
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…
In this paper we obtain some possibilistic variants of the probabilistic laws of large numbers, different from those obtained by other authors, but very natural extensions of the corresponding ones in probability theory. Our results are…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…