论文标题
在多元分数随机字段上：回火和操作员稳定的法律
On multivariate fractional random fields: tempering and operator-stable laws
论文作者
论文摘要
在本文中，我们定义了一个新的，广泛的矢量值随机字段，称为钢化操作员分数稳定的随机场（TRF，简称为TRF）。 TRF通常是非高斯，并且概括了钢化部分的稳定随机过程。 TRF包括通过回火（矩阵 - ）均质的，矩阵值构造的移动平均值和可和谐的亚类，相对于矢量值，严格操作员稳定的随机稳定随机测量，在时间和傅立叶域内和傅立叶域随机积分中构建。我们确定了TRF的存在和基本属性。假设高斯性和各向同性均表明TRF的某些移动平均值与可和谐的子类之间的等效性。此外，我们在数个高斯实例的标量值情况下建立样本路径属性。
In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable random fields (TRF, for short). TRF is typically non-Gaussian and generalizes tempered fractional stable stochastic processes. TRF comprises moving average and harmonizable-type subclasses that are constructed by tempering (matrix-) homogeneous, matrix-valued kernels in time- and Fourier-domain stochastic integrals with respect to vector-valued, strictly operator-stable random measures. We establish the existence and fundamental properties of TRF. Assuming both Gaussianity and isotropy, we show the equivalence between certain moving average and harmonizable subclasses of TRF. In addition, we establish sample path properties in the scalar-valued case for several Gaussian instances.
