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Poissonian process 
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#1
Apr2314, 04:34 PM

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? 


#2
Apr2314, 07:19 PM

P: 160

Just like before, you have to solve the differential equation [itex]P'(t) = \omega(t)P(t)[/itex]. The general solution is [itex]P(t) = \exp\left(\int_0^t \omega(u)\,du\right).[/itex]



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