Laplace transforms and suprema of stochastic processes - Klaus Schürger (University of Bonn, Bonn Graduate School of Economics (BGSE), 2002)
It is shown that moments of negative order as well as positive non- integral order of a nonnegative random variable X can be expressed by the Laplace transform of X. Applying these results of certain first passage times gives explicit formulae for moments of suprema of Bessel processes as well as strictly stable Levy processes having no positive jumps.
Keywords: G12; 330; Laplace transform; Bessel process; Lévy process; Stochastischer Prozess; Theorie