Statistics Seminar: Mehlman -- Structure and Moving Average Representation for Strongly Harmonizable Processes

Harmonizable Process can be thought of as Fourier transforms of vector--valued 
measures.  If the vector--valued measure has orthogonal increments, the 
harmonizable processes so obtained is stationary.  Much of what is known about 
linear prediction and stationary processes has been generalized to harmonizable 
processes.  This talk will review what has been done in this area.

The classical moving average representation of stationary processes is 
generalized to moving average representations for discrete and continuous 
multidimensional strongly harmonizable processes.  Necessary and sufficient 
conditions on covariance functions are given for the existence of such moving 
average representations.

The study of strongly harmonizable processes is amiable to Fourier analytic 
methods and is of interest in applications such as prediction theory, 
filtering problems and others.