相关论文: Mixtures in non stable Levy processes

In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the…

This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density.…

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…

Constructing \Levy-driven Ornstein-Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the \emph{a-reminder}…

The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for…

We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…

Consider a multivariate L\'evy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving L\'evy process is from a parametric family. We derive the likelihood function assuming that the innovation term is…

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…

We investigate the distributional properties of two generalized Ornstein-Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to…

Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…

Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…

We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…

The class of Levy processes for which overshoots are almost surely constant quantities is precisely characterized.

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized…

We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…

The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the…

In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…

The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and applications. We present here a construction of multifractional multistable processes, based…

We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…

We consider an Ornstein-Uhlenbeck process with values in R^n driven by a L\'evy process (Z_t) taking values in R^d with d possibly smaller than n. The L\'evy noise can have a degenerate or even vanishing Gaussian component. Under a…