Does stationarity of Poisson processes mean $\Bbb P(N(s,t]) = \Bbb P(N(s+h,t+h])$?

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I am supposed to find the probability for some given $s,t,h > 0$, the probability $$N(s,t] = N (s+h,t+h] +m$$ for $m\in\Bbb N$.

I am confused by this however because I thought stationarity meant $N(s,t] = N (s+h,t+h] = k$.

Doesn't having a constant $m$ violate this?