I have a one-dimensional diffusion on $[0,1]$ and I need to calculate the distribution of the first exit time of the interval $(-\epsilon,\epsilon)$ for an $\epsilon > 0$. A good first step would be to find the distribution for a corresponding first exit time for the standard Brownian motion. Then using the speed and scale of the process, it should hopefully be possible to translate the result to the diffusion case. I guess the first exit time of an interval should be something relatively well known for the Wiener process. Could you direct me to any good references? Obviously, if you know a reference where this is discussed for diffusions, it would be even nicer. Thanks!
2026-03-30 07:03:48.1774854228
Distribution of the first exit time of a one-dimensional diffusiom/ Brownian motion
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