A remark about the norm of a Brownian bridge (Q1771429)

It is well-known that the Euclidean norm of an \(n\)-dimensional Brownian motion provides an \(n\)-dimensional Bessel process. This paper proves that, unless conditioned at zero, the law of the Euclidean norm of an \(n\)-dimensional bridge is merely equivalent rather than equal to that of an \(n\)-dimensional Bessel bridge. Explicit mutual density between these laws is presented. Relations between Brownian bridges and Bessel processes with drifts are also considered.