A random vector X with representation X = ∑ j≥0 AjZj is considered. Here, (Zj) is a sequence of independent and identically distributed random vectors and (Aj) is a sequence of random matrices, ‘predictable’ with respect to the sequence (Zj). The distribution of Z1 is assumed to be multivariate regular varying. Moment conditions on the matrices (Aj) are determined under which the distribution o...

Abstract. We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly ...

In this paper, the relation between synchronization and control of chaotic nodes connected through a time–varying network is discussed. In particular, the effects of pinning control on a set of moving chaotic agents are investigated showing that the role of system parameters, like agent density, is critical in order to reach the synchronous behavior and also to control the whole network by pinn...

In this paper, we study the asymptotic behaviour of tail probability number customers in steady-state M/G/1 retrial queue with Bernoulli schedule, under assumption that service time distribution has a regularly varying tail. Detailed properties are obtained for conditional (priority) and orbit, respectively, terms recently proposed exhaustive stochastic decomposition approach. Numerical example...

This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting-time and/or sojourn-time distribution, demonstrating that different disciplines lead to quite different tail behavior. The orientation of the paper is methodological: We outline four different methods for determining tail...

In this paper we present a new type of multivariate distributions for asset returns which we call the multi-tail elliptical distributions. Multi-tail elliptical distribution can be thought to be an extension of the elliptical distributions that allow for varying tail parameters. We present a two-step random mechanism leading to this new type of distributions. In particular, this mechanism is de...

The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze extremal dependence of the copulas that are specified only by densities. The relation between the cop...