• Corpus ID: 245006117

# Solving the hyperbolic Anderson model 1: Skorohod setting

@inproceedings{Chen2021SolvingTH,
title={Solving the hyperbolic Anderson model 1: Skorohod setting},
author={Xia Chen and Aur'elien Deya and Jian Song and Samy Tindel},
year={2021}
}
• Published 9 December 2021
• Mathematics
This paper is concerned with a wave equation in dimension d ∈ {1, 2, 3}, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the space-time covariance of the Gaussian noise, allowing the existence and uniqueness of a mild Skorohod solution.
3 Citations

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. We study a wave equation in dimension d ∈ { 1 , 2 } with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions

## References

SHOWING 1-10 OF 17 REFERENCES

### Hyperbolic Anderson Model with space-time homogeneous Gaussian noise

• Mathematics
• 2016
In this article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\sigma(u)=u$, also known in the literature as the Hyperbolic

### The Non-Linear Stochastic Wave Equation in High Dimensions

• Mathematics
• 2008
We propose an extension of Walsh's classical martingale measure stochastic integral that makes it possible to integrate a general class of Schwartz distributions, which contains the fundamental

### Fractional stochastic wave equation driven by a Gaussian noise rough in space

• Mathematics
Bernoulli
• 2020
In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional

### The Stochastic Wave Equation with Multiplicative Fractional Noise: A Malliavin Calculus Approach

We consider the stochastic wave equation with multiplicative noise, which is fractional in time with index H > 1/2, and has a homogeneous spatial covariance structure given by the Riesz kernel of

### Exact asymptotics of the stochastic wave equation with time-independent noise

• Mathematics
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 2022
In this article, we study the stochastic wave equation in all dimensions $d\leq 3$, driven by a Gaussian noise $\dot{W}$ which does not depend on time. We assume that either the noise is white, or

### 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

### On a non-linear 2D fractional wave equation

We pursue the investigations initiated in [Aur{\'e}lien Deya: A non-linear wave equation with fractional perturbation (2017)] about a wave-equation model with quadratic perturbation and stochastic

### 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

### Moment estimates for some renormalized parabolic Anderson models

• Mathematics
The Annals of Probability
• 2021
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: \$\partial_{t} u_{t}(x) = \frac12 \Delta u_{t}(x) + u_{t}(x) \, \dot