I try to solve the master equation for the Poisson process. For this I have to check that $$P_{ik}(t)=0 \;\;\forall t \geq0, \;\;\text{when }k<i $$ The explanation is given as follow: $$\frac{dP_{i0}(t)}{dt}=-\lambda P_{i0}(t)$$ with $P_{i0}(0)=0$, if $i \neq 0$. Hence we can conclude $P_{i0}(t)=0$, $\forall t \geq 0$. Why is this the case that we conclude that? It should be verry trivial but I can't see it... Many thanks for some help!
2026-04-01 05:43:48.1775022228
Master equation of the Poisson Process
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