7 citations · 37 across the 20 of their papers we have counts for
24 papers
On variation functions of lacunary series
Matyas Barczy, Peter Kern
We study variation functions of some lacunary series along the sequence of -adic partitions, where is an integer. By such a lacunary series, we mean that in the definition…
Max-semistable extremal behavior of AR(1)-processes connected with Bernoulli convolutions
Peter Kern, Alef Sterk
We consider simple autoregressive processes of type AR(1), whose stationary distribution is supported on a subset of the unit interval and is an affine transformation of a Bernoull…
Cutting a Cake Is Not Always a 'Piece of Cake': A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory
Peter Kern, Daniel Neugebauer, Jörg Rothe +3
Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and arti…
On self-similar Bernstein functions and corresponding generalized fractional derivatives
Peter Kern, Svenja Lage
We use the theory of Bernstein functions to analyze power law tail behavior with log-periodic perturbations which corresponds to self-similarity of the Bernstein functions. Such ta…
Space-time duality for semi-fractional diffusions
Peter Kern, Svenja Lage
Almost sixty years ago Zolotarev proved a duality result which relates an -stable density for to the density of a -stable distribution on the positive real…
Semi-fractional diffusion equations
Peter Kern, Svenja Lage, Mark M. Meerschaert
It is well known that certain fractional diffusion equations can be solved by the densities of stable Lévy motions. In this paper we use the classical semigroup approach for Lévy p…
On the carrying dimension of occupation measures for self-affine random fields
Peter Kern, Ercan Sönmez
Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for…
On exact Hausdorff measure functions of operator semistable Lévy processes
Peter Kern, Lina Wedrich
Let be an operator semistable Lévy process on with exponent , where is an invertible linear operator on . In this paper we…
Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties
Peter Kern, Mark M. Meerschaert, Yimin Xiao
This paper proves sharp bounds on the tails of the Lévy exponent of an operator semistable law on . These bounds are then applied to explicitly compute the Hausdorff a…
An integral representation of dilatively stable processes with independent increments
Thorsten Bhatti, Peter Kern
Dilative stability generalizes the property of selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. Inspir…
Dilatively semistable stochastic processes
Peter Kern, Lina Wedrich
Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It…
Dilatively stable stochastic processes and aggregate similarity
Matyas Barczy, Peter Kern, Gyula Pap
Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Iglói…
On some compound distributions with Borel summands
Helmut Finner, Peter Kern, Marsel Scheer
The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett a…
Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes
Matyas Barczy, Peter Kern
We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explici…
A link between Bougerol's identity and a formula due to Donati-Martin, Matsumoto and Yor
Matyas Barczy, Peter Kern
We point out an easy link between two striking identities on exponential functionals of the Wiener process and the Wiener bridge originated by Bougerol, and Donati-Martin, Matsumot…
Operator scaled Wiener bridges
Matyas Barczy, Peter Kern, Vincent Krause
We introduce operator scaled Wiener bridges by incorporating a matrix scaling in the drift part of the SDE of a multidimensional Wiener bridge. A sufficient condition for the bridg…
The dimension of the St. Petersburg game
Peter Kern, Lina Wedrich
Let be the total gain in repeated St.\ Petersburg games. It is known that converges in distribution to a random element along subsequences o…
A general multiparameter version of Gnedenko's transfer theorem
Peter Kern
Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with ind…
Correction: Limit theorems for coupled continuous time random walks
Peter Kern, Mark M. Meerschaert, Hans-Peter Scheffler
Correction to "Limit theorems for coupled continuous time random walks" (Ann. Probab. 32 (2004) 730-756).
Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes
Adam Barczyk, Peter Kern
A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a ju…
Hausdorff dimension of operator semistable Lévy processes
Peter Kern, Lina Wedrich
Let be an operator semistable Lévy process in $\rd$ with exponent , where is an invertible linear operator on $\rd$ and is semi-selfsimilar with re…
General alpha-Wiener bridges
Matyas Barczy, Peter Kern
An alpha-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter alpha>0 represents a mean reversion force to zero. We generalize the notion…
Sample path deviations of the Wiener and the Ornstein-Uhlenbeck process from its bridges
Matyas Barczy, Peter Kern
We study sample path deviations of the Wiener process from three different representations of its bridge: anticipative version, integral representation and space-time transform. Al…
Representations of multidimensional linear process bridges
Matyas Barczy, Peter Kern
We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representati…