Is there a distance metric that we can use to see how close are two point processes?
If instead of point process, we deal with random variables, there are a bunch of distance metrics that we can use to see how close are they based on their probability density function such as relative entropy ( Kullback-Leibler divergence) and total variation distance. But, for point processes, this doesn't sound simple.
Since the number of arrivals for a point process is a random variable, one way I thought about is using distance metrics on the number of arrivals of the point processes. But, I think since number of arrivals is not a complete representation of a point process, we are missing some information about the closeness of those point processes, if we just use their number of arrival. Can you please let me know your ideas how I should proceed?
Also, please let me know any nice references to read.