Related papers: Minimal thinness with respect to symmetric L\'evy …
In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…
In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this…
We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $\Gamma$ is a finite disjoint union…
We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with…
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
For each $n \geq 1$, let $\{X_{j,n}\}_{1 \leq j \leq n}$ be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process…
In this short note we study homogenization of symmetric $d$-dimensional L\'evy processes. Homogenization of one-dimensional pure jump Markov processes has been investigated by Tanaka \emph{et al.} in 1992; their motivation was the work by…
We wish to characterise when a L\'{e}vy process $X_t$ crosses boundaries like $t^\kappa$, $\kappa>0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarrow 0}|X_t|/t^{\kappa}$, $\limsup_{t\downarrow…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
We characterize the number of points for which there exist non-empty Terracini sets of points in $\mathbb{P}^n$. Then we study minimally Terracini finite sets of points in $\mathbb{P}^n$ and we obtain a complete description in the case of…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
The first step to study lower bounds for a stochastic process is to prove a special property - Sudakov minoration. The property means that if a certain number of points from the index set are well separated then we can provide an optimal…
In this note we prove that minimal networks enjoy minimizing properties for the length functional. A minimal network is, roughly speaking, a subset of $\mathbb{R}^2$ composed of straight segments joining at triple junctions forming angles…
We study the density of the supremum of a strictly stable L\'evy process. We prove that for almost all values of the index $\alpha$ -- except for a dense set of Lebesgue measure zero -- the asymptotic series which were obtained in A.…
We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.
We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…
The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that…