Suppose I have a compound poisson process with arrival rate x and variance V such that V > 1. Further suppose the original process is split into two processes with proportion p and 1-p. The arrival rate into the first split is xp and x(1-p) into the second, but how can I calculate the variance?
Simulation tells me that the variance in the split process is less than the original process but not proportional to p or 1-p.