Related papers: Double hypergeometric L\'evy processes and self-si…
In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…
By killing a stable L\'{e}vy process when it leaves the positive half-line, or by conditioning it to stay positive, or by conditioning it to hit 0 continuously, we obtain three different positive self-similar Markov processes which…
Ba\~nuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse the asymptotic tail distribution of the first time a stable (L\'evy) process in dimension $d\geq 2$ exists a cone. We use these results to develop the notion of a…
We compare two definitions of multistable L\'evy motions. Such processes are extensions of classical L\'evy motion where the stability index is allowed to vary in time. We show that the two multistable L\'evy motions have distinct…
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 consider some special classes of L\'evy processes with no gaussian component whose L\'evy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1) dx$, where $\nu$ is the density of the stable L\'evy measure and $\gamma$ is a positive…
The Lamperti--Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, there is a Markov additive process (MAP). In the case that the rssMp is taken to…
We define a notion of Markov process indexed by curves drawn on a compact surface and taking its values in a compact Lie group. We call such a process a two-dimensional Markovian holonomy field. The prototype of this class of processes, and…
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…
A series of conjectures is obtained as further investigation of the integral transformation I(alpha) introduced in the previous paper. A Macdonald-type difference operator D is introduced. It is conjectured that D and I(alpha) are…
Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a class of functions closely related to Nevanlinna-Pick functions and complete Bernstein functions. The name 'Rogers functions' is proposed for this class. Under…
This work deals with a family of Hardy-Sobolev doubly critical system defined in $\mathbb{R}^n$. More precisely, we provide a classification of the positive solutions, whose expressions comprise multiplies of solutions of the decoupled…
We give a complete classification of a certain family of step functions related to the Nyman--Beurling approach to the Riemann hypothesis and previously studied by V. I. Vasyunin. Equivalently, we completely describe when certain sequences…
Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov process is one where probability can…
A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and…
L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how…
This work concerns the Ornstein-Uhlenbeck type process associated to a positive self-similar Markov process $(X(t))_{t\geq 0}$ which drifts to $\infty$, namely $U(t):= {\rm e}^{-t}X({\rm e}^t-1)$. We point out that $U$ is always a…
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary…
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…
The present paper is an addendum to the paper ``L\'evy models amenable to efficient calculations", where we introduced a general class of Stieltjes-L\'evy processes (SL-processes) and signed SL processes defined in terms of certain…