Related papers: A strong ergodic theorem for extreme and intermedi…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…
We prove an L^1 subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally L^1-good sequences nearly as sparse as the set of squares. In the process, we prove that…
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random…
Let $\{(X_i,Y_i)\}$ be a stationary ergodic time series with $(X,Y)$ values in the product space $\R^d\bigotimes \R .$ This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in…
We formulate an ergodic theory for the (almost sure) limit $\mathcal{P}^\text{co}_{\tilde{\mathcal{E}}}$ of a sequence $(\mathcal{P}^\text{co}_{\mathcal{E}_n})$ of successive dynamic imprecise probability kinematics (DIPK, introduced in…
We consider a point process sequence induced by a stationary symmetric alpha-stable (0 < alpha < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
The bounds for absolute moments of order statistics are established. Let $X_1,\dots ,X_n$ be independent identically distributed real-valued random variables and let $X_{1:n}\le \dots \le X_{n:n}$ be the corresponding order statistics. The…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first…
We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking…
Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way.…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…