MULTISCALE REPRESENTATION AND ESTIMATION OF FRACTAL POINT-PROCESSES

Fractal point processes have a potentially important role to play in t he modeling of a wide range of natural and manmade phenomena. However, the lack of a suitable framework for their representation has frequen tly made their application in many problems difficult. We introduce na tural multiscale representations for an important class of these proce sses based on mixtures of Poisson processes. In turn, this framework l eads to efficient new algorithms for both the synthesis and the analys is of such processes. These include algorithms for optimal fractal dim ension and interarrival time estimation that are of interest in a rang e of applications. Several aspects of the performance of these algorit hms are also addressed.