$S_{t} = X_{1} + X_{2} + ... + X_{Nt}$ is a compound Poisson process. I know that when $X_{j}$ can only take value 0 or 1, $S_{t}$ is also Poisson process.
I can understand when $X_{j}$ = 1 for all j, $S_{t}$ is a Poisson Process. But why when some of $X_{j}$ = 0, $S_{t}$ is also Poisson Process?