Multiscale representation and estimation of fractal point processes

Fractal point processes have a potentially important role to play in the modeling of a wide range of natural and man-made phenomena. However, the lack of a suitable framework for their representation has frequently made their application in many problems difficult. We introduce natural multiscale representations for an important class of these processes based on mixtures of Poisson processes. In turn, this framework leads to efficient new algorithms for both the synthesis and the analysis of such processes. These include algorithms for optimal fractal dimension and interarrival time estimation that are of interest in a range of applications. Several aspects of the performance of these algorithms are also addressed.