4 citations · 16 across the 12 of their papers we have counts for
13 papers
Invertible Complex Measures on Euclidean Spaces
David Berger, Alexander Lindner
In 1971 Taylor characterised all complex measures on that are invertible with respect to convolution as those which can be written in the form $δ_γ\ast σ^{\ast m} \ast…
The Liouville theorem for a class of Fourier multipliers and its connection to coupling
David Berger, René L. Schilling, Eugene Shargorodsky
The classical Liouville property says that all bounded harmonic functions in , i.e.\ all bounded functions satisfying , are constant. In this paper we obtain…
Almost periodic stationary processes
David Berger, Farid Mohamed
We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for inf…
Quasi-infinite divisibility of a class of distributions with discrete part
David Berger, Merve Kutlu
We consider distributions on that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribu…
Second order elliptic partial differential equations driven by Lévy white noise
David Berger, Farid Mohamed
This paper deals with linear stochastic partial differential equations with variable coefficients driven by Lévy white noise. We first derive an existence theorem for integral tran…
On multivariate quasi-infinitely divisible distributions
David Berger, Merve Kutlu, Alexander Lindner
A quasi-infinitely divisible distribution on is a probability distribution on whose characteristic function can be written as the quotient of the…
The (strong) Liouville property for a class of non-local operators
David Berger, René L. Schilling
We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Com…
A Cramér--Wold device for infinite divisibility of -valued distributions
David Berger, Alexander Lindner
We show that a Cramér--Wold device holds for infinite divisibility of -valued distributions, i.e. that the distribution of a -valued random vector i…
Lévy driven linear and semilinear stochastic partial differential equations
David Berger
The goal of this paper is twofold. In the first part we will study Lévy white noise in different distributional spaces and solve equations of the type , where $p…
Lévy driven CARMA generalized processes and stochastic partial differential equations
David Berger
We give a new definition of a Lévy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give suffi…
Central Limit Theorems for Moving Average Random Fields with Non-Random and Random Sampling On Lattices
David Berger
For a Lévy basis on and a suitable kernel function , consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R…
On the integral modulus of infinitely divisible distributions
David Berger
We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part…
On Quasi-Infinitely Divisible Distributions with a Point Mass
David Berger
An infinitely divisible distribution on is a probability measure such that the characteristic function has a Lévy-Khintchine representation with characteri…