# 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} }

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

### Necessary and sufficient conditions to solve parabolic Anderson model with rough noise

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We obtain necessary and sufficient conditions for the existence of n-th chaos of the solution to the parabolic Anderson model ∂ ∂t u(t, x) = 1 2 ∆u(t, x) + u(t, x)Ẇ (t, x), where Ẇ (t, x) is a…

### Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting

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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…

### Central limit theorems for heat equation with time-independent noise: the regular and rough cases

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In this article, we investigate the asymptotic behaviour of the spatial integral of the solution to the parabolic Anderson model with time independent noise in dimension d ≥ 1, as the domain of the…

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