Related papers: Exit identities for L\'evy processes observed at P…

In this paper we analyse time change equations (TCEs) for L\'evy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial value problems (IVPs) which are easier to handle. Properties…

This paper is concerned with the behaviour of a L\'{e}vy process when it crosses over a positive level, $u$, starting from 0, both as $u$ becomes large and as $u$ becomes small. Our main focus is on the time, $\tau_u$, it takes the process…

In this paper, we derive the joint Laplace transforms of occupation times until its last passage times as well as its positions. Motivated by Baurdoux [2], the last times before an independent exponential variable are studied. By applying…

For one-dimensional symmetric L\'{e}vy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is either a single point or an interval. The estimates are…

A general connection between the characteristic function of a L\'evy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events…

Using a very simple argument based on the indepenence of increments and the fact that in a finite dimensional space $R^{d}$ there are not too many directions, we derive a theorem stating that exit time of any (non-constant) L\'{e}vy process…

The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…

For spectrally positive L\'evy processes killed on exiting the half-line, existence of a quasi-stationary distribution is characterized by the exponential integrability of the exit time, the Laplace exponent and the non-negativity of the…

The simple L\'evy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the…

For a spectrally positive strictly stable process with index in (1,2), the paper obtains i) the density of the time when the process makes first exit from an interval by hitting the interval's lower end point before jumping over its upper…

A two-sided exit problem is solved for a difference of a compound Poisson process and a compound renewal process. More precisely, the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the…

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 review some of the theory relevant to passage times of one-dimensional L\'evy processes out of bounded regions, highlighting results that are useful in physical phenomena modelled by heavy-tailed L\'evy flights. The process is…

We establish a connection between the scattering inverse problem and the determination of the distribution of the position of the Levy process at the exit time of a bounded interval in term of its Levy exponent.

We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…

We present a numerical scheme to calculate fluctuation identities for exponential L\'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult…

We study a first passage time of a L\'evy process over a positive constant level. In the spectrally negative case we give conditions for absolutely continuity of the distributions of the first passage times. The tail asymptotics of their…

We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty}…

Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…

Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…