Multi-dimensional smoothing transformations: Existence, regularity and stability of fixed points
Multi-dimensional smoothing transformations: Existence, regularity and stability of fixed points
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多维平滑变换：不动点的存在性、规律性和稳定性
DOI：
10.1016/j.spa.2013.07.006
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发表时间：
2014
影响因子：
1.4
通讯作者：
D. Matthes
中科院分区：
文献类型：
--
作者：
F. Bassetti;D. Matthes
分析了多维空间中概率度量的一类光顺变换。综合运用概率方法和傅立叶分析，证明了有限二阶矩的概率测度类内不动点的存在唯一性，刻画了它是一个尺度混合的高斯分布，并讨论了它的正则性。我们还对它的尾巴进行了分类，这可能是帕累托型的。作为应用，我们研究了一类Kac型动力学模型驻定解的稳定性。特别地，我们证明了吸引域是有限二阶矩的概率测度。
We analyze a class of smoothing transformations on probability measures in multiple space dimensions. Applying a synthesis of probabilistic methods and Fourier analysis, we prove existence and uniqueness of a fixed point inside the class of probability measures of finite second moment, characterize it as a scale mixture of Gaussians, and discuss its regularity. We also classify its tail, which might be of Pareto type. As an application, we study the stability of stationary solutions in a Kac-type kinetic model. In particular, we prove that the domain of attraction is precisely the probability measures of finite second moment.
影响因子：
2
作者：
Bassetti, Federico;Ladelli, Lucia;Matthes, Daniel
通讯作者：
Matthes, Daniel
影响因子：
2.4
作者：
Duering, Bertram;Matthes, Daniel;Toscani, Giuseppe
通讯作者：
Toscani, Giuseppe