arXiv subjects

Wolfgang Hörmann

Publications and source records attributed to Wolfgang Hörmann.

3 recordsLinked to original sources

arXiv2026

A Distributional Approach to Generalized Stochastic Processes on Locally Compact Abelian Groups

This paper is dedicated to Paul Butzer on the occasion of his 85th birthday. His work and example have strongly influenced not only the first author, but also generations of mathematicians working in approximation theory and Fourier analysis. He has shown younger colleagues the importance of remaining open to applied areas, avoiding an overly narrow scope, and exploring different ways of understanding mathematical facts. A recurring theme in his work is the logical equivalence of fundamental statements in analysis. It may be less widely known that, besides his central role in approximation theory, Paul Butzer has also made significant contributions to probability theory. We hope that he will enjoy this note, which shows that a purely functional-analytic treatment of generalized stochastic processes is possible. The approach is based on the Segal algebra S0(G) and avoids several technical difficulties associated with the customary framework of vector-valued integration and topological vector spaces.

math.FA↗

arXiv2020

Assessing Intervention Strategies for Non Homogeneous Populations Using a Closed Form Formula for R0

A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number $R_0$, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual $R_0$" that is the expected number of secondary cases for a given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual $R_0$ values. Also an intelligent vaccination plan for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R0 values.

q-bio.PE↗

arXiv2012

Simulating the Continuation of a Time Series in R

The simulation of the continuation of a given time series is useful for many practical applications. But no standard procedure for this task is suggested in the literature. It is therefore demonstrated how to use the seasonal ARIMA process to simulate the continuation of an observed time series. The R-code presented uses well-known modeling procedures for ARIMA models and conditional simulation of a SARIMA model with known parameters. A small example demonstrates the correctness and practical relevance of the new idea.

stat.CO↗