Related papers: Heavy-tailed Distributions In Stochastic Dynamical…

The study of heavy-tailed distributions in economic and financial systems has been widely addressed since financial time series has become a research subject.After the eighties, several "highly improbable" market drops were observed (e.g.…

We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…

We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…

Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…

Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an…

We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…

Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by…

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…

Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period of time…

It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such…