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Suppose I have a kinetic model for a stochastic system of three states, as shown in the attachment. I solve for the probability distribution of the first passage time from A to B and I get the distribution shown on the right hand side.

I can understand that if there is a peak in the distribution, we can say there is some most probable first time(fpt) for the system to transit from A to B because in the path A->C->B, one can go back and fourth between A and C before reaching B. But how about the non-zero peak at t=0 in the distribution? I know it comes from the path A->B because this path has no intermediate stop, the distribution follows a single exponential function but I am confused about how to interpret it physically. Does it means that the system 'typically' takes 0 time to transit to B in this path?

And if I want to have a estimation of the most probable fpt, is taking the weighted mean of the two peaks with respect to their probabilities a reasonable approach?

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# Interpretation of the first passage time

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