Deconvolution of point processes
arXiv:1202.0951
Abstract
The superposition of two independent point processes can be described by multiplication of their probability generating functionals (p.g.fl.s). The inverse operation, which can be viewed as a deconvolution, is defined by dividing the superposed process by one of its constituent p.g.fl.s. The deconvolved process is computed using the higher-order chain rule for Gateaux differentials. The higher-order quotient rule for Gateaux differentials is first established and then applied to point processes.