منابع مشابه
Moments of 2d Parabolic Anderson Model
In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.
متن کاملChaos Expansion of 2d Parabolic Anderson Model
We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the density function of the annealed polymer in a white noise environment.
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 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 کاملA Singular Parabolic Anderson Model
We consider the following stochastic partial differential equation: ∂u ∂t = 1 2 ∆u + κu ˙ F , for x ∈ R d in dimension d ≥ 3, where ˙ F (t, x) is a mean zero Gaussian noise with the singular covariance E ˙ F (t, x) ˙ F (t, y) = δ(t − s) |x − y| 2. Solutions u t (dx) exist as singular measures, under suitable assumptions on the initial conditions and for sufficiently small κ. We investigate vari...
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: Asymptotic Analysis
سال: 2018
ISSN: 1875-8576,0921-7134
DOI: 10.3233/asy-171460