6 citations · 11 across the 10 of their papers we have counts for
11 papers
A Poisson representation of the positive sojourn time of Lévy processes
Helmut H. Pitters
We study the distribution of the positive sojourn time of an arbitrary Lévy process . For an exponential random var…
Levy's second arcsine law via the ballot theorem
Helmut H. Pitters
We provide a new and elementary proof of Levy's second arcsine law for Brownian motion. The only tools required are basic properties of Brownian motion and Poisson processes, and t…
Occupation times and areas derived from random sampling
Frank Aurzada, Leif Döring, Helmut H. Pitters
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we…
Mod- convergence of Stirling distributions and limit theorems for zeros of their generating functions
Zakhar Kabluchko, Alexander Marynych, Helmut Pitters
We study mod- convergence of several probability distributions on the set of positive integers that involve Stirling numbers of both kinds and, as a consequence, derive various…
Poisson limit for the number of cycles in a random permutation and the number of segregating sites
Helmut H. Pitters, Philip Weissmann
Consider a random permutation of drawn according to the Ewens measure with parameter and let denote the number of its cycles…
The number of cycles in a random permutation and the number of segregating sites jointly converge to the Brownian sheet
Helmut Pitters
Consider a random permutation of drawn according to the Ewens measure with parameter and let denote the number of its cycles…