ON THE REMARKABLE DISTRIBUTIONS OF MAXIMA OF SOME
FRAGMENTS OF THE STANDARD REFLECTING RANDOM WALK AND
BROWNIAN MOTION
Abstract: In this paper, we consider some distributions of maxima of excursions and related
variables for standard random walk and Brownian motion. We discuss the infinite
divisibility properties of these distributions and calculate their Lévy measures.
Lastly we discuss Chung’s remark related with Riemann’s zeta functional equation.
2000 AMS Mathematics Subject Classification: 60E07, 60G40, 60G50, 60J25, 60J55,
60J65, 60J75.
Key words and phrases: Standard random walk, standard Brownian motion, excursion,
meander, comeander, infinite divisibility, Lévy measure, arcsine law, Riemann’s zeta
function.