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May 6, 2021 at 21:43 comment added HMPanzo When either the starting or ending point is 0, then the Euclidean norm of the Brownian bridge and the corresponding Bessel bridge have the same law as processes. When both starting and ending points aren't 0, then these laws are absolutely continuous with an explicit mutual density. See the 2004 paper A remark about the norm of a Brownian bridge by Yor and Zambotti.
May 6, 2021 at 7:19 comment added Mateusz Kwaśnicki A comment to the last paragraph: I guess for the Bessel bridge some results are available, but the norm of the Brownian bridge is not the Bessel bridge.
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May 6, 2021 at 3:28 history asked Tuvasbien CC BY-SA 4.0