• Corpus ID: 250089335

Moment Intermittency in the PAM with Asymptotically Singular Noise

@inproceedings{Lamarre2022MomentII,
title={Moment Intermittency in the PAM with Asymptotically Singular Noise},
author={Pierre Yves Gaudreau Lamarre and Promit Ghosal and Yuchen Liao},
year={2022}
}
• Published 27 June 2022
• Mathematics
Let ξ be a singular Gaussian noise on R that is either white, fractional, or with the Riesz covariance kernel; in particular, there exists a scaling parameter ω > 0 such that cξ(c·) is equal in distribution to ξ for all c > 0. Let (ξε)ε>0 be a sequence of smooth mollifications such that ξε → ξ as ε → 0. We study the asymptotics of the moments of the parabolic Anderson model (PAM) with noise ξε as ε → 0, both for large (i.e., t → ∞) and fixed times t. This approach makes it possible to study the…

References

SHOWING 1-10 OF 43 REFERENCES

Stationary parabolic Anderson model and intermittency

• Mathematics
• 1995
SummaryThis paper is devoted to the analysis of the large time behavior of the solutions of the Anderson parabolic problem: $$\frac{{\partial u}}{{\partial t}} = \kappa \Delta u\xi (x)u$$ when the

Moment asymptotics for parabolic Anderson equation with fractional time-space noise: In Skorokhod regime

. In this paper, we consider the parabolic Anderson equation that is driven by a Gaussian noise fractional in time and white or fractional in space, and is solved in a mild sense deﬁned by Skorokhod

Almost sure asymptotics for the continuous parabolic Anderson model

• Mathematics
• 2000
Abstract. We consider the parabolic Anderson problem ∂tu = κΔu + ξ(x)u on ℝ+×ℝd with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constant and ξ is a random homogeneous potential. We

Moment asymptotics for the continuous parabolic Anderson model

• Mathematics
• 2000
We consider the parabolic Anderson problem ∂ t u = κ(cid:5)u + ξ (cid:3) x (cid:4) u on R + × R d with initial condition u (cid:3) 0 (cid:9)x (cid:4) = 1. Here ξ (cid:3)·(cid:4) is a random shift-

Parabolic Anderson model with rough or critical Gaussian noise

• Xia Chen
• Mathematics
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 2019
This paper considers the parabolic Anderson equation ∂u ∂t = 1 2 u + u ∂ d+1WH ∂t∂x1 · · · ∂xd generated by a (d + 1)-dimensional fractional noise with the Hurst parameter H = (H0,H1, . . . ,Hd). The

The Parabolic Anderson Model

• Mathematics
• 2016
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 ℤd. We first introduce the model

Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency

• Mathematics
• 2014
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of

Moment estimates for some renormalized parabolic Anderson models

• Mathematics
The Annals of Probability
• 2021