= Difference of independent Poisson processes
{title2=$X_t=N_t^+-N_t^-$}
For independent <Poisson processes> with rates $r_+,r_-\geq0$, their difference is a <Lévy process> with <characteristic function> $\exp(t[r_+(e^{iu}-1)+r_-(e^{-iu}-1)])$. When the combined rate is positive, its jumps occur at rate $r_++r_-$, with direction probabilities proportional to the two rates. Equal unit rates give $\exp(2t(\cos u-1))$ and a rate-two <Compound Poisson process> with <Rademacher distribution> jumps. Its paths are integer-valued, <càdlàg>, and of <finite variation> on compact intervals.
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