Related papers: Meromorphic Levy processes and their fluctuation i…
Markov processes are well understood in the case when they take place in the whole Euclidean space. However, the situation becomes much more complicated if a Markov process is restricted to a domain with a boundary, and then a satisfactory…
The class of Levy processes for which overshoots are almost surely constant quantities is precisely characterized.
We first introduce and derive some basic properties of a two-parameters family of one-sided Levy processes. Their Laplace exponents are given in terms of the Pochhammer symbol. This family includes, in a limit case, the family of Brownian…
We present a new approach to fluctuation identities for reflected L\'{e}vy processes with one-sided jumps. This approach is based on a number of easy to understand observations and does not involve excursion theory or It\^{o} calculus. It…
Levy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. A typical model is obtained by considering finite dimensional linear stochastic SISO systems driven…
In this paper approximation methods for infinite-dimensional Levy processes, also called (time-dependent) Levy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional…
Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of…
We consider the regularity of sample paths of Volterra-L\'{e}vy processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$ where $X$ is a L\'{e}vy process and $F$ is a…
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.
Exponential L\'evy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such…
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…
In contrast to their seemingly simple and shared structure of independence and stationarity, L\'evy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes.…
We consider a pair of coupled queues driven by independent spectrally-positive Levy processes. With respect to the bi-variate workload process this framework includes both the coupled processor model and the two-server fluid network with…
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder…
In the recent paper \cite{Ng5} we have introduced a method of studying the multi-dimensional Kingman convolutions and their associated stochastic processes by embedding them into some multi-dimensional ordinary convolutions which allows to…
The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor…
In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…
What is the analogue of L\'evy processes for random surfaces? Motivated by scaling limits of random planar maps in random geometry, we introduce and study L\'evy looptrees and L\'evy maps. They are defined using excursions of general L\'evy…
Stochastic Loewner Evolutions (SLE) with a multiple sqrt(kappa)B of Brownian motion B as driving process are random planar curves (if kappa<=4) or growing compact sets generated by a curve (if kappa>4). We consider here more general Levy…
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…