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首页> 外文会议>Seminar on Stochastic Analysis, Random Fields, and Applications >Recent Advances Related to SPDEs with Fractional Noise
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Recent Advances Related to SPDEs with Fractional Noise

机译：最近与具有分数噪声的SPDES相关的进展

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We review the literature related to stochastic partial differential equations with spatially-homogeneous Gaussian noise, and explain how one can introduce the structure of the fractional Brownian motion into the temporal component of the noise. The Hurst parameter H is assumed to be greater than 1/2. In the case of linear equations, we revisit the conditions for the existence of a mild solution. In the nonlinear case, we point out what are the difficulties due to the fractional component of the noise. These difficulties can be avoided in the case of equations with multiplicative noise, since in this case, the solution has a known Wiener chaos decomposition. Finally, this methodology is applied to the wave equation (in arbitrary dimension d > 1), driven by a Gaussian noise which has a spatial covariance structure given by the Riesz kernel.
机译：我们审查了与空间 - 均匀高斯噪声的随机偏微分方程相关的文献，并解释了如何将分数褐色运动的结构引入噪声的时间分量。假设HUST参数H大于1/2。在线性方程的情况下，我们重新审视存在温和溶液的条件。在非线性情况下，我们指出了由于噪声的分数组分导致的困难是什么。在具有乘法噪声的方程的情况下，可以避免这些困难，因为在这种情况下，解决方案具有已知的维纳混沌分解。最后，该方法应用于波动方程（在任意尺寸D> 1）上，由具有由RIESZ内核给出的空间协方差结构的高斯噪声驱动。

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