Abstract
Using a Gaussian estimate, we prove an upper bound on the almost-sure large time exponential growth of the solution to the parabolic Anderson model {equation presented} on the lattice Zd when the potential V(t} x) is a mean zero Gaussian field that is white in time and homogeneous in space. As the diffusivity parameter K tends to 0, our upper bound is of the same order as the lower bound given by Carmona and Molchanov in [2].
Original language | English (US) |
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Pages (from-to) | 43-49 |
Number of pages | 7 |
Journal | Random Operators and Stochastic Equations |
Volume | 4 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1996 |
All Science Journal Classification (ASJC) codes
- Analysis
- Statistics and Probability