论文标题
广义时空分数随机动力学方程
Generalized space-time fractional stochastic kinetic equation
论文作者
论文摘要
在本文中，我们在$ \ mathbb {r}^d $中研究了一类非线性时空分数随机动力学方程，该方程与高斯噪声一样，是白色的，在太空中是白色的。这种类型的方程构成了涉及时间上的分数衍生物的非线性随机热方程的延伸，而空间中的分数则延伸。我们为解决方案的存在和独特性提供了必要的条件。我们还研究了解决方案的各种特性：路径规律性，第二刻的行为以及在线性添加噪声的情况下的平稳性。
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the non-linear stochastic heat equation involving fractional derivative in time and fractional Laplacian in space. We give a necessary condition on the spatial covariance for the existence and uniqueness of the solution. We also study various properties of the solution: path regularity, the behavior of second moment and the stationarity in the case of linear additive noise.
