Point processes on the complex plane with applications
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI SYSTEM AT REQUEST OF AUTHOR.] A point process is a random collection of points from a certain space, and point process models are widely used in areas dealing with spatial data. However, studies of point process theory in the past only focused on Euclidean spaces, and point processes on the complex plane have been rarely explored. In this thesis we introduce and study point processes on the complex plane. We present several important quantities of a complex point process (CPP) that investigate first and second order properties of the process. We further introduce the Poisson complex point process and model its intensity function using log-linear and mixture models in the corresponding 2-dimensional space. The methods are exemplified via applications to density approximation and time series analysis via the spectral density, as well as construction and estimation of covariance functions of Gaussian random fields.
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