We consider the Stochastic Partial Differential Equation [equation presented] The potential is assumed to be Gaussian white noise in time, stationary in space. We obtain the asymptotics of the almost sure Lyapunov exponent γ(k) for the solution as k→0. Namely γ(k)∼c0/ln(1/ k), where the constant C0 is determined by the correlation function of the potential.
All Science Journal Classification (ASJC) codes
- Statistics and Probability