Moments of an exponential functional of random walks and permutations with given descent sets

Tamas Szabados, Balazs Szekely

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial $Y=1+{\xi }_1+{\xi }_1{\xi }_2+{\xi }_1{\xi }_2{\xi }_3+...$ of independent and identicall…