 Meeting time of two independent Brownian motions

ID: meeting-time-of-two-independent-brownian-motions

Two independent one-dimensional Brownian motions started at

- a

and

a

meet at the first time a Brownian motion started at

2 a

hits zero. The meeting time has density

f_{T} (u) = \frac{a}{π u ^{3}} e^{- a^{2} / u}, u > 0.

An orthogonal sum coordinate is independent of this hitting time and makes the meeting position conditionally

N (0, u /2)

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