# Poissonian process

by aaaa202
Tags: poissonian, process
 P: 1,005 I think the classical Poissonian process is where you have something, which in a time dt has a probability ωdt. Then one can show quite easily that the probability that the "something" has not yet decayed goes as P(t)=exp(-ωt), because it obeys a differential equation with the given solution. However, what does P(t) look like if ω is time dependent?
 P: 160 Just like before, you have to solve the differential equation $P'(t) = -\omega(t)P(t)$. The general solution is $P(t) = \exp\left(-\int_0^t \omega(u)\,du\right).$

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