Moment asymptotics for the continuous parabolic Anderson model
نویسندگان
چکیده
منابع مشابه
Temporal asymptotics for fractional parabolic Anderson model
In this paper, we consider fractional parabolic equation of the form ∂u ∂t = −(−∆) α 2 u+ uẆ (t, x), where −(−∆)α2 with α ∈ (0, 2] is a fractional Laplacian and Ẇ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result ...
متن کاملThe Parabolic Anderson Model
This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice Z. We first introduce the model and give heuristic explanations of the long-time behavior of the solution, both in the annealed and the quenched setting for time-independent potentials. We thereby consider examples of potentials st...
متن کاملAnnealed Asymptotics for the Parabolic Anderson Model with a Moving Catalyst
This paper deals with the solution u to the parabolic Anderson equation ∂u/∂t = κ∆u+ξu on the lattice Zd. We consider the case where the potential ξ is time-dependent and has the form ξ(t, x) = δ0(x − Yt) with Yt being a simple random walk with jump rate 2d̺. The solution u may be interpreted as the concentration of a reactant under the influence of a single catalyst particle Yt. In the first pa...
متن کامل4 the Parabolic Anderson Model
This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice Z. We first introduce the model and give heuristic explanations of the long-time behavior of the solution, both in the annealed and the quenched setting for time-independent potentials. We thereby consider examples of potentials st...
متن کاملLyapunov Exponents for the Parabolic Anderson Model
We consider the asymptotic almost sure behavior of the solution of the equation u(t, x) = u0(x) + κ ∫ t
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2000
ISSN: 1050-5164
DOI: 10.1214/aoap/1019737669