A General Class of Models for Stationary Two-Dimensional Random Processes
提出了一类平稳空间过程的谱密度-协方差函数参数族，协方差函数为第二类修正贝塞尔函数的线性组合，并利用随机微分方程提供物理基础，为二维过程识别与估计建立类似一维有理谱密度/自回归移动平均方法的通用理论。
A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle, 1963). Recursive computation techniques make calculation of the covariance functions feasible for even the most complicated models. Stochastic differential equations are used to provide a physical basis for the models as well as to develop methods for generation of the resultant processes. The results provide a step toward development of a general theory and methodology for the identification and estimation of two-dimensional processes to parallel the rational spectral density/autoregressive-moving average approach for one-dimensional processes.