New answers tagged brownian-motion
1
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PDE for the probability of Brownian motion staying in an area (reference request)
I think your idea ("PS") works fine, at least when $A$ has finite measure and is a moderately reasonable set (let's say open) and probably in general with more effort. It does seem to get a ...
2
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PDE for the probability of Brownian motion staying in an area (reference request)
The easiest way to show this is to check that if $\hat{u}$ is a bounded solution to your boundary value problem, then $\hat{u}(t-s,B_{s\wedge\tau}+x)$ is a martingale, where $\tau$ is the minimum of ...
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