Basic Theory of Random Measures and Point Processes
This chapter sets out a framework for developing point process theory as part of a general theory of random measures. This framework was developed during the 1940s and 1950s, and reached a definitive form in the now classic treatments by Moyal (1962) and Harris (1963). It still provides the basic framework for describing point processes both on the line and in higher-dimensional spaces, including especially the treatment of finite-dimensional distributions, moment structure, and generating functionals. In the intervening decades, many important alternative approaches have been developed for more specialized classes of processes, particularly those with an evolutionary structure, and we come to some at least of these in later chapters.
KeywordsPoint Process Random Measure Counting Measure Dirichlet Process Moment Measure
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