Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 90, 630090, Russia
Abstract:
Let M∞ be the supremum of a random walk drifting to -∞ which is generated by the partial sums of a sequence of independent identically distributed random variables with a common distribution F. We prove that the moment generating function E exp(sM∞) is a rational function if and only if the function ∫0∞ exp(sx)F(dx) is rational.