论文标题
用时差噪声击中一般分数动力学方程的特性
Hitting properties of generalized fractional kinetic equation with time-fractional noise
论文作者
论文摘要
本文研究了由高斯噪声分数驱动的广义分数动力学方程系统的系统，在太空中是白色或有色的。我们得出了连续性的均方模量和解决方案的一些二阶特性。这些用于推导下层和上限的概率，而路径过程则根据$ \ mathfrak {g} _q $ -capacity和$ g_q $ -hhhausdorff措施击中有限的Borel集合，这产生了点击点的关键维度。此外，基于对解决方案的和谐表示的一些精细分析，我们证明所有点在临界维度中都是极性的。这为Hinojosa-Calleja和Sanz-Solé[Stoch pde：Anal Comp（2022）中提出的猜想提供了有力的证据。 https://doi.org/10.1007/s40072-021-00234-6]。
This paper studies hitting properties for the system of generalized fractional kinetic equations driven by Gaussian noise fractional in time and white or colored in space. We derive the mean square modulus of continuity and some second order properties of the solution. These are applied to deduce lower and upper bounds for probabilities that the path process hits bounded Borel sets in terms of the $\mathfrak{g}_q$-capacity and $g_q$-Hausdorff measure, respectively, which yield the critical dimension for hitting points. Further, based on some fine analysis of the harmonizable representation for the solution, we prove that all points are polar in the critical dimension. This provides strong evidence for the conjecture raised in Hinojosa-Calleja and Sanz-Solé [Stoch PDE: Anal Comp (2022). https://doi.org/10.1007/s40072-021-00234-6].
