Related papers: Right inverses of L\'{e}vy processes

This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…

A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We…

We show that if a L\'evy process creeps then, as a function of $u$, the renewal function $V(t,u)$ of the bivariate ascending ladder process $(L^{-1},H)$ is absolutely continuous on $[0,\infty)$ and left differentiable on $(0,\infty)$, and…

For v\in R^n let K be a compact set in R^n containing a suitable smooth surface and such that the intersection {tv+x:t\in R}\cap K is a closed interval or a single point for all x\in K. We prove that every linear first order differential…

A necessary and sufficient condition for a L\'evy process $X$ to stay positive, in probability, near 0, which arises in studies of Chung-type laws for $X$ near 0, is given in terms of the characteristics of $X$.

A L\'evy processes resurrected in the positive half-line is a Markov process obtained by removing successively all jumps that make it negative. A natural question, given this construction, is whether the resulting process is absorbed at 0…

Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int\_0^\infty e^{-\xi\_{t-}} d\eta\_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy processes for which (the distribution of)…

We consider a process $Z$ on the real line composed from a L\'evy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of $Z$ seen from its supremum, the supremum $\overline Z$…

We consider the exponential functional $A_{\infty}=\int_0^{\infty} e^{\xi_s} ds$ associated to a Levy process $(\xi_t)_{t \geq 0}$. We find the asymptotic behavior of the tail of this random variable, under some assumptions on the process…

Consider a spectrally positive L\'evy process $Z$ with log-Laplace exponent $\Psi$ and a positive continuous function $R$ on $(0,\infty)$. We investigate the entrance from $\infty$ of the process $X$ obtained by changing time in $Z$ with…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

We construct the law of L\'{e}vy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of…

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…

A refracted L\'evy process is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted…

We consider a L\'evy process that starts from $x<0$ and conditioned on having a positive maximum. When Cram\'er's condition holds, we provide two weak limit theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the first…

The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…

Let $X$ be a real L\'evy process and let $\Xpos $ be the process conditioned to stay positive. We assume that $ 0 $ is regular for $(-\infty, 0)$ and $(0, +\infty) $ with respect to $X$. Using elementary excursion theory arguments, we…

For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…

We develop a general construction for nonlinear L\'evy processes with given characteristics. More precisely, given a set $\Theta$ of L\'evy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process…

We study the skewness premium (SK) introduced by Bates (1991) in a general context using L\'evy Processes. Under a symmetry condition Fajardo and Mordecki (2006) obtain that SK is given by the Bate's $x%$ rule. In this paper we study SK…