Related papers: More on hypergeometric Levy processes
We derive explicitly the coupling property for the transition semigroup of a L\'{e}vy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the…
We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…
We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process $X$ in $\mathbf{R}^d$, and a new class of energy forms and their corresponding capacities. We…
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 establish a novel characterisation of the law of the convex minorant of any L\'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of…
Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature,…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
We classify L\'evy processes according to the solution spaces of the associated parabolic PIDEs. This classification reveals structural characteristics of the processes and is relevant for applications such as for solving PIDEs numerically…
The goal of this paper is threefold. First, we survey the existing results on Hunt's hypothesis (H) for Markov processes and Getoor's conjecture for L\'{e}vy processes. Second, we investigate (H) for multidimensional L\'{e}vy processes from…
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…
Based on the concept of a L\'evy copula to describe the dependence structure of a multivariate L\'evy process we present a new estimation procedure. We consider a parametric model for the marginal L\'evy processes as well as for the L\'evy…
We introduce Ising-H\"usler-Reiss processes, a new class of multivariate L\'evy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability…
Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of…
Taking account of recent developments in the representation of $d$-dimensional isotropic stable L\'evy processes as self-similar Markov processes, we consider a number of new ways to condition its path. Suppose that $\Omega$ is a region of…
Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.
For $n$ equidistant observations of a L\'evy process at time distance $\Delta_n$ we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal-Getoor index in a non- or semiparametric manner.…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…
We develop the information geometry of L\'evy processes. Deriving $\alpha$-divergences directly in terms of the L\'evy triplets of the L\'evy processes, we identify Fisher information matrix and $\alpha$-connection on the statistical…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…