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.
Citation
Alexei Borodin. Ivan Corwin. "Moments and Lyapunov exponents for the parabolic Anderson model." Ann. Appl. Probab. 24 (3) 1172 - 1198, June 2014. https://doi.org/10.1214/13-AAP944
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