On the expected maximum of a birth-and-death process

Videla, Leonardo

Keywords: Birth-and-death processes, inverse binomial, maximum distribution

Abstract

We describe a simple continuous time process obtained by pointwise addition of finitely many i.i.d. 0–1 processes with alternating exponential regimes. We investigate the asymptotic mean value of the maxima (the peaks) reached within the non-zero zones. In this short communication we show that the computation of this quantity leads to a transcendental equation that, to the best of our knowledge, has not appeared before in the literature.

Más información

Título de la Revista: STATISTICS AND PROBABILITY LETTERS
Volumen: 159
Editorial: Elsevier
Fecha de publicación: 2019
Idioma: Inglés
URL: https://doi.org/10.1016/j.spl.2019.108665