Related papers: Large deviation estimates involving deformed expon…

Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…

We study tail probabilities via some Gaussian approximations. Our results make refinements to large deviation theory. The proof builds on classical results by Bahadur and Rao. Binomial distributions and their tail probabilities are…

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…

There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…

In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…

Consider the partition function of a directed polymer in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is a well-known fact that the free energy of the…

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…

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…

In order to account for large variance and fat tail of damage by natural disaster, we study a simple model by combining distributions of disaster and population/property with their spatial correlation. We assume fat-tailed or power-law…

Condensation phenomena are ubiquitous in nature and are found in condensed matter, disordered systems, networks, finance, etc. In the present work we investigate one of the best frameworks in which condensation phenomena take place, namely,…

Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…

We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…

Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…

We study the large deviation probabilities of infinite weighted sums of independent random variables that have stretched exponential tails. This generalizes Kiesel and Stadtm\"uller (2000), who study the same objects under the assumption of…

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…

We consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…