Related papers: Dilatively stable stochastic processes and aggrega…

In this note we prove the well-posedness for stochastic 2D Navier-Stokes equation driven by general L\'evy processes (in particular, $\alpha$-stable processes), and obtain the existence of invariant measures.

We extend the result of Nualart and Schoutens on chaotic decomposition of the $L^2$-space of a L\'evy process to the case of a generalized stochastic processes with independent values.

We consider some special classes of L\'evy processes with no gaussian component whose L\'evy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1) dx$, where $\nu$ is the density of the stable L\'evy measure and $\gamma$ is a positive…

In this paper, we establish the existence of transition density for geometric $\alpha$-stable processes by using the property of self-decomposability--a fundamental concept in the theory of L\'evy processes. In contrast to traditional and…

The index Whittaker convolution operator, recently introduced by the authors, gives rise to a convolution measure algebra having the property that the convolution of probability measures is a probability measure. In this paper, we introduce…

This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen's and Wirtinger's inequalities, as…

We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…

This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit c\`adl\`ag modifications and derive bounds on their local…

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often…

We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Koml\'{o}s-Major-Tusn\'{a}dy type are obtained.…

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…

In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…

Multistable processes are tangent at each point to a stable process, but where the index of stability and the index of localisability varies along the path. In this work, we give two estimators of the stability and the localisability…

This paper studies new classes of infinitely divisible distributions on R^d. Firstly, the connecting classes with a continuous parameter between the Jurek class and the class of selfdecomposable distributions are revisited. Secondly, the…

We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…

This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…

Integrable systems are usually given in terms of functions of continuous variables (on ${\mathbb R}$), functions of discrete variables (on ${\mathbb Z}$) and recently in terms of functions of $q$-variables (on ${\mathbb K}_{q}$). We…

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…