Small Kappa Asymptotics of the Almost Sure Lyapunov Exponent for the Continuum Parabolic Anderson Model

Michael Rael

Published 2012-09-13, updated 2013-03-15Version 3

We prove that the almost sure Lyapunov exponent \lambda(\kappa) of the continuous space Parabolic Anderson Model is bounded above by $c_u \kappa^{1/3}$ as $\kappa\downarrow0$ under mild regularity conditions. This bound of the same order of the previously proven lower bound, $\lambda(\kappa) \ge c_l \kappa^{1/3}$.