Poisson Distribution - Occurrence - Multi-dimensional Poisson Process

Multi-dimensional Poisson Process

The poisson distribution arises as the distribution of counts of occurrences of events in (multidimensional) intervals in multidimensional Poisson processes in a directly equivalent way to the result for unidimensional processes. This,is D is any region the multidimensional space for which |D|, the area or volume of the region, is finite, and if N(D) is count of the number of events in D, then