Relating the almost-sure Lyapunov exponent of a parabolic SPDE and its coefficients’ spatial regularity
نویسنده
چکیده
We derive a lower bound on the large-time exponential behavior of the solution to a stochastic parabolic partial differential equation on R+ × R 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.
منابع مشابه
Asymptotics for the Almost Sure Lyapunov Exponent for the Solution of the Parabolic Anderson Problem
We consider the Stochastic Partial Differential Equation ut = κ∆u+ ξ(t, x)u, t ≥ 0, x ∈ Z . 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(κ) for the solution as κ → 0. Namely γ(κ) ∼ c0 ln(1/κ) , where the constant c0 is determined by the correlation function of the potential.
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