2017/03/29 by Joseph Mecke, Mecke, Joseph, Werner Nagel +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #60E10 #60G55 #Diffusion and Search Dynamics #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1703.10000
openalex publication_date 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Summarizing results from Joseph Mecke's last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept of thickening of a random variable, as an inverse operation to thinning (which is usually applied to point processes) is introduced, based on generating functions, and a characterization of thickable random variables is given. Further, some new relations between exponential distributions and their interpretation in terms of Poisson point processes are derived with the help of the Laplace transform.