Related papers: On extrema of stable processes

We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…

The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…

In this paper the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running…

Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function $f \ge 0$. From an application point of view, one is rather interested in extreme loss events that occur relative to…

We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider…

In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…

The paper studies a class of Ornstein-Uhlenbeck processes on the classical Wiener space. These processes are associated with a diffusion type Dirichlet form whose corresponding diffusion operator is unbounded in the Cameron-Martin space. It…

A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for…

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type. This leads to the solution of analogous extremal…

We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.

We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results…

For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…

Let $\mathbb{X}=(\mathbb{X}_t)_{t\geq 0}$ be the subdiffusive process defined, for any $t\geq 0$, by $ \mathbb{X}_t = X_{\ell_t}$ where $X=(X_t)_{t\geq 0}$ is a L\'evy process and $\ell_t=\inf \{s>0;\: \mathcal{K}_s>t \}$ with…

We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…

In this article, the infinite series form of the probability densities of tempered stable and inverse tempered stable subordinators are obtained using Mellin transform. Further, the densities of the products and quotients of stable and…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ together with a sequence of independent, identically distributed $X$-space valued random variables $\xi_1,\dots,\xi_n$ and give a good estimate on the…

A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter $\omega\in [-1,1]$ are iteratively added. Besides masses (or primary…

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…