Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
sorry, this is my clarification for how I expected the difference P1-P2 behave: since the jump of Poisson process is 1, the difference of 2 Poisson processes should evolve around 0 with the jump of either 1 or -1. Therefore, h(t) will have the jump of 0.5 or -0.5 when the difference is not 0