We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sum...

Consider two M=G=1 queues that are coupled in the following way. Whenever both queues are non-empty, each server serves its own queue at unit speed. However, if server 2 has no work in its own queue, then it assists server 1, resulting in an increased service speed r 1 1 in the first queue. This kind of coupling is related to generalized processor sharing. We assume that the service request dis...

In this paper, we propose to identify the dependence structure that exists between returns on equity and commodity futures and its development over the past 20 years. The key point is that we do not impose any dependence structure, but let the data select it. To do so, we model the dependence between commodity (metal, agriculture and energy) and stock markets using a flexible approach that allo...

the relationship between live body weight, body length, girth circumference, animal hight, upper, middle as well as lower width of fat-tail, fat-tail length, fat-tail gap length, fat-tail depth and fat-tail circumference along with fat-tail weight were determined using records of 731 loribakhtiari sheep. principal component and least square analyses were applied to solve the collinearity instab...

Let X and Y be two nonnegative and dependent random variables following a generalized Farlie–Gumbel–Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY . We quantify the impact as the limit, as x → ∞, of the quotient of Pr(XY > x) and Pr(XY ∗ > x), where X and Y ∗ are independent random variables identically distribut...

We introduce a new type of estimator for the spectral tail process regularly varying time series. The approach is based on characterizing invariance property process, which incorporated into via projection technique. show uniform asymptotic normality this estimator, both in case known and unknown index regular variation. In simulation study procedure shows more stable performance than previousl...

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that th...

In this thesis we contribute to the understanding of the pivotal role of the temporal dimension in networked social systems, previously neglected and now uncovered by the data revolution recently blossomed in this field. To this aim, we first introduce the time-varying networks formalism and analyze some empirical data of social dynamics, extensively used in the rest of the thesis. We discuss t...

| The random-code capacity region of the multiple-access arbitrarily varying channel subject to both state and input constraints is determined. Consideration of a simple erasure channel shows that the capacity region is not convex in general.

The spread of an infection on a real-world social network is determined by the interplay of two processes – the dynamics of the network, whose structure changes over time according to the encounters between individuals, and the dynamics on the network, whose nodes can infect each other after an encounter. Physical encounter is the most common vehicle for the spread of infectious diseases, but d...