Related papers: Right inverses of Levy processes: the excursion me…

Trawl processes belong to the class of continuous-time, strictly stationary, infinitely divisible processes; they are defined as Levy bases evaluated over deterministic trawl sets. This article presents the first nonparametric estimator of…

We develop new representations for the Levy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these…

For spectrally negative L\'evy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find…

We investigate the behavior of L\'{e}vy processes with convolution equivalent L\'{e}vy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial…

The central result of this paper is an analytic duality relation for real-valued L\'evy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the L\'evy process…

We ask for necessary and sufficient conditions for almost sure finiteness of the perpetual integrals of a Levy process. Zero-one laws are already known for Brownian motion with drift and spectrally one-sided Levy processes. Under the…

This thesis develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally…

We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Levy process. We further consider the Brownian motion of a fractal particle,…

Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a L\'evy insurance risk process under the Cram\'er-Lundberg and convolution equivalent conditions. For example, the limiting distributions…

We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of L\'evy walks, in which transport is driven by a convex combination of fractional material derivatives and a source…

In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…

In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…

Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…

During the last decade Levy processes with jumps have received increasing popularity for modelling market behaviour for both derviative pricing and risk management purposes. Chan et al. (2009) introduced the use of empirical likelihood…

In this article, we introduce a new definition of bankruptcy for a spectrally negative L\'evy insurance risk process. More precisely, we study the Gerber-Shiu distribution for a ruin model where at each time the surplus goes negative, an…

A random walk starts from the origin of a d-dimensional lattice. The occupation number n(x,t) equals unity if after t steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sums M(t) of observables…

As well known, all functionals of a Markov process may be expressed in terms of the generator operator, modulo some analytic work. In the case of spectrally negative Markov processes however, it is conjectured that everything can be…

Consider a Langevin process, that is an integrated Brownian motion, constrained to stay on the nonnegative half-line by a partially elastic boundary at 0. If the elasticity coefficient of the boundary is greater than or equal to a critical…

L\'evy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, L\'evy flights for light in…