Related papers: Tail Behavoir of sums of random components

In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…

In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…

We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as…

We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant…

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

This paper describes limiting behaviour of tail empirical process associated with long memory stochastic volatility models. We show that such process has dichotomous behaviour, according to an interplay between a Hurst parameter and a tail…

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…

This paper considers the tail asymptotics for a cumulative process $\{B(t); t \ge 0\}$ sampled at a heavy-tailed random time $T$. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality…

Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…

We investigate the asymptotic behavior of sample functions of stable processes when $t{\to}\infty$. We compare our results with the iterated logarithm law, results for the first hitting time and most visited sites problems.

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

In the paper, we investigate the asymptotic behaviors of the randomly weighted sums with upper tail asymptotically independent increments under new conditions without requiring moment assumptions on random weights.An application of the…

We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…

Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…