Related papers: Mixing properties of multivariate infinitely divis…

We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…

This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…

We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity…

For a given pair of positive integers $d$ and $N$ with $N \geq 2$, for strictly stationary random fields that are indexed by the $d$-dimensional integer lattice and satisfy $N$-tuplewise independence, the dependence coefficients associated…

Mixture models have been widely used in modeling of continuous observations. For the possibility to estimate the parameters of a mixture model consistently on the basis of observations from the mixture, identifiability is a necessary…

We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary…

Gibbs distribution of binary Markov random fields on a sparse on average graph is considered in this paper. The strong spatial mixing is proved under the condition that the `external field' is uniformly large or small. Such condition on…

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense…

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields…

Incomplete binary mixing of two components can form a heterogeneous assemblage in space. The heterogeneity power spectrum of the assemblage can be frequently obtained. However, it is unknown if a stochastic binary field exists to generate…

Notions of weak and uniformly weak mixing (to zero) are defined for bounded sequences in arbitrary Banach spaces. Uniformly weak mixing for vector sequences is characterized by mean ergodic convergence properties. For bounded sequences,…

It is proved that infinitesimal triangular arrays obtained from normalized partial sums of strongly mixing (but not necessarily stationary) random sequences, can produce as lilmits only selfdecomposable distributions.

We prove that a stationary max--infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max--infinitely divisible processes.

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in H\"older spaces. Strong mixing and $\rho$-mixing conditions are investigated as well as $\tau$-dependent…

We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We…

A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…

We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…

For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…