# Marked poisson process vs compounded

I am a bit fuzzy about difference between compounded poisson process defined as $$\sum_{i=1}^{N_t} D_i$$ where $N_t$ is poisson process and $D_i$ are iid random variables

and marked poisson process. Is compounded poisson a version of marked process $\{(\tau_i, D_i), i \in \mathbb{N} \}$ ?

• My opinion: A poisson counting process jumps up by one unit at random times. A compound poisson process is a generalization of this, which jumps up (or down) by a random amount, i.e. not always +1. The increments however are independent. In a marked poisson process, the "mark" has a certain prob distribution, but it is not necessarily equal to the previous mark plus/minus a random amount. The notion of "counting" or incrementatio is no longer there. – noob2 Nov 17 '17 at 19:23