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- W2962897626 abstract "We study a $d$-dimensional wave equation model ($2leq dleq4$) with quadratic nonlinearity and stochastic forcing given by a space-time fractional noise. Two different regimes are exhibited, depending on the Hurst parameter $H=(H_{0},ldots,H_{d})in(0,1)^{d+1}$ of the noise: If $sum_{i=0}^{d}H_{i}>d-frac{1}{2}$, then the equation can be treated directly, while in the case $d-frac{3}{4}<sum_{i=0}^{d}H_{i}leq d-frac{1}{2}$, the model must be interpreted in the Wick sense, through a renormalization procedure. Our arguments essentially rely on a fractional extension of the considerations of [Trans. Amer. Math. Soc. 370 (2017) 7335–7359] for the two-dimensional white-noise situation, and more generally follow a series of investigations related to stochastic wave models with polynomial perturbation." @default.
- W2962897626 created "2019-07-30" @default.
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- W2962897626 date "2019-05-01" @default.
- W2962897626 modified "2023-09-25" @default.
- W2962897626 title "A nonlinear wave equation with fractional perturbation" @default.
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- W2962897626 doi "https://doi.org/10.1214/18-aop1296" @default.
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