Chernoff's density is log-concave.
We show that the density ofZ= argmax{W (t)-t2}, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.
Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Paris, France.
Fadoua
F
Balabdaoui
Department of Statistics, University of Washington, Seattle, WA 98195-4322, USA.
Jon A
JA
Wellner
Brownian motion; Polya frequency function; Prekopa–Leindler theorem; Schoenberg’s theorem; airy function; correlation inequalities; hyperbolically monotone; log-concave; monotone function estimation; slope process; strongly log-concave