Relating the almost-sure Lyapunov exponent of a parabolic SPDE and its Coefficients' spatial regularity

摘要

We derive a lower bound on the large-time exponential behavior of the solution to a stochastic parabolic partial differential equation on R(+)xR in the case of a spatially homogeneous Gaussian potential that is white-noise in time, and study the relation between the lower bound and the potential's spatial modulus of continuity.