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Poissonian process

by aaaa202
Tags: poissonian, process
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aaaa202
#1
Apr23-14, 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?
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eigenperson
#2
Apr23-14, 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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