Poisson processes and a log-concave Bernstein theorem
Volume 247 / 2019
Studia Mathematica 247 (2019), 85-107
MSC: Primary 26D15; Secondary 44A10.
DOI: 10.4064/sm180212-30-7
Published online: 5 November 2018
Abstract
We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the Prékopa–Leindler and the Walkup theorems. One of our main tools is a stochastic variational formula for the Poisson average.
