Moments and lyapunov exponents for the parabolic anderson model

Abstract

We study the parabolic Anderson model in (1+1) dimensions with nearest neighbor jumps and space-time white noise (discrete space/continuous time). We prove a contour integral formula for the second moment and compute the second moment Lyapunov exponent. For the model with only jumps to the right, we prove a contour integral formula for all moments and compute moment Lyapunov exponents of all orders. © Institute of Mathematical Statistics, 2014.