Related papers: Tail Behavior of Randomly Weighted Sums
The sums and maxima of non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraint is that there exists a unique series in a…
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…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
A random variable $\xi$ has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (\lambda \xi) <\infty$ for some $\lambda >0$, and has a {\it heavy-tailed} distribution (is…
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
In this paper, we examine two problems on applied probability, which are directly connected with the dependence in presence of heavy tails. The first problem, is related to max-sum equivalence of the randomly weighted sums in bi-variate set…
The tail behavior of aggregates of heavy-tailed random vectors is known to be determined by the so-called principle of "one large jump'', be it for finite sums, random sums, or, L\'evy processes. We establish that, in fact, a more general…
In this paper we consider a heavy-tailed stochastic volatility model, $X_t=\sigma_tZ_t$, $t\in\mathbb{Z}$, where the volatility sequence $(\sigma_t)$ and the i.i.d. noise sequence $(Z_t)$ are assumed independent, $(\sigma_t)$ is regularly…
We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…
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…
Let $\eta_1$, $\eta_2,\ldots$ be independent copies of a random variable $\eta$ with zero mean and finite variance which is bounded from the right, that is, $\eta\leq b$ almost surely for some $b>0$. Considering different types of the…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…
In this paper we analyze a branching process with immigration defined recursively by $X_t=\theta_t\circ X_{t-1}+B_t$ for a sequence $(B_t)$ of i.i.d. random variables and random mappings $ \theta_t\circ x:=\theta_t(x)=\sum_{i=1}^xA_i^{(t)},…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
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 this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…
We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…
A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…
A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…