Related papers: A short memory condition for infinitely divisible …

In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.

Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined. The measures are expressed as the sum of lagged dependence and instantaneous dependence.…

We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…

We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

We study a framework where the hypothesis of a minimum length in space-time is complemented with the notion of reference frame invariance. It turns out natural to interpret the action of the obtained reference frame transformations in the…

This note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is based on the scarceness of long edges in the graph and weak…

We consider a purely fractionally deferenced process driven by a periodically time-varying long memory parameter. We will build an estimate for the vector parameters using the minimum Hellinger distance estimation. The results are…

In the previous paper [Nenashev et al., arXiv:0912.3161] an analytical theory confirmed by numerical simulations has been developed for the field-dependent hopping diffusion coefficient D(F) in one-dimensional systems with Gaussian…

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable…

Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and…

We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is…

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…

We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. The rates are computed explicitly. We show…

M-dependence is a commonly used assumption in the study of dependent sequences. In this paper, central limit theorems for m-dependent random variables under the sub-linear expectations are established based mainly on the conditions of…

Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…

We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property…

We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any…