Related papers: Extended Factorizations of Exponential Functionals…

For a L\'evy process $\xi=(\xi_t)_{t\geq0}$ drifting to $-\infty$, we define the so-called exponential functional as follows \[{\rm{I}}_{\xi}=\int_0^{\infty}e^{\xi_t} dt.\] Under mild conditions on $\xi$, we show that the following…

In this paper we study the Wiener-Hopf factorization for a class of L\'evy processes with double-sided jumps, characterized by the fact that the density of the L\'evy measure is given by an infinite series of exponential functions with…

We establish a new integral equation for the probability density of the exponential functional of a L\'evy process and provide a three-term (Wiener-Hopf type) factorisation of its law. We explain how these results complement the techniques…

In this paper we introduce a ten-parameter family of L\'{e}vy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and…

With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric L\'evy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of a…

Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting…

We study the Wiener-Hopf factorization for L\'evy processes $X_t$ with completely monotone jumps. Extending previous results of L.C.G. Rogers, we prove that the space-time Wiener-Hopf factors are complete Bernstein functions of both the…

This note provides a factorization of a L\'evy pocess over a phase-type horizon $\tau$ given the phase at the supremum, thereby extending the Wiener-Hopf factorization for $\tau$ exponential. One of the factors is defined using time…

We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as…

We prove that the spatial Wiener-Hopf factorisation of a L\'evy process or random walk without killing is unique.

We study the Wiener--Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener--Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such…

Suppose $X_{t}$ is a one-dimensional and real-valued L\'evy process started from $X_0=0$, which ({\bf 1}) its nonnegative jumps measure $\nu$ satisfying $\int_{\Bbb R}\min\{1,x^2\}\nu(dx)<\infty$ and ({\bf 2}) its stopping time $\tau(q)$ is…

We study the Wiener-Hopf factorization for Levy processes with bounded positive jumps and arbitrary negative jumps. Using the results from the theory of entire functions of Cartwright class we prove that the positive Wiener-Hopf factor can…

This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…

We study the distribution of the negative Wiener-Hopf factor for a class of two-sided jumps L\'evy processes whose positive jumps have a rational Laplace transform. The positive Wiener-Hopf factor for this class of processes was studied by…

The last couple of years has seen a remarkable number of new, explicit examples of the Wiener-Hopf factorization for Levy processes where previously there had been very few. We mention in particular the many cases of spectrally negative…

There is an abundance of useful fluctuation identities for one-sided L\'evy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix…

Exponential functionals of L\'evy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process.…

Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Levy process Z above a positive level a. In this paper it is shown that the law of T(a) can be approximated arbitrarily closely by the laws of…

Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose…